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href="#L910">910</a><a id="L911" href="#L911">911</a><a id="L912" href="#L912">912</a><a id="L913" href="#L913">913</a><a id="L914" href="#L914">914</a><a id="L915" href="#L915">915</a><a id="L916" href="#L916">916</a><a id="L917" href="#L917">917</a><a id="L918" href="#L918">918</a><a id="L919" href="#L919">919</a><a id="L920" href="#L920">920</a><a id="L921" href="#L921">921</a><a id="L922" href="#L922">922</a><a id="L923" href="#L923">923</a><a id="L924" href="#L924">924</a><a id="L925" href="#L925">925</a><a id="L926" href="#L926">926</a><a id="L927" href="#L927">927</a><a id="L928" href="#L928">928</a><a id="L929" href="#L929">929</a><a id="L930" href="#L930">930</a><a id="L931" href="#L931">931</a><a id="L932" href="#L932">932</a><a id="L933" href="#L933">933</a><a id="L934" href="#L934">934</a><a id="L935" href="#L935">935</a><a id="L936" href="#L936">936</a><a id="L937" href="#L937">937</a><a id="L938" href="#L938">938</a><a id="L939" href="#L939">939</a><a id="L940" href="#L940">940</a><a id="L941" href="#L941">941</a><a id="L942" href="#L942">942</a><a id="L943" href="#L943">943</a><a id="L944" href="#L944">944</a><a id="L945" href="#L945">945</a><a id="L946" href="#L946">946</a><a id="L947" href="#L947">947</a><a id="L948" href="#L948">948</a><a id="L949" href="#L949">949</a><a id="L950" href="#L950">950</a><a id="L951" href="#L951">951</a><a id="L952" href="#L952">952</a><a id="L953" href="#L953">953</a><a id="L954" href="#L954">954</a><a id="L955" href="#L955">955</a><a id="L956" href="#L956">956</a><a id="L957" href="#L957">957</a><a id="L958" href="#L958">958</a><a id="L959" href="#L959">959</a><a id="L960" href="#L960">960</a><a id="L961" href="#L961">961</a><a id="L962" href="#L962">962</a><a id="L963" href="#L963">963</a><a id="L964" href="#L964">964</a><a id="L965" href="#L965">965</a><a id="L966" href="#L966">966</a><a id="L967" href="#L967">967</a><a id="L968" href="#L968">968</a><a id="L969" href="#L969">969</a><a id="L970" href="#L970">970</a><a id="L971" href="#L971">971</a><a id="L972" href="#L972">972</a><a id="L973" href="#L973">973</a><a id="L974" href="#L974">974</a><a id="L975" href="#L975">975</a><a id="L976" href="#L976">976</a><a id="L977" href="#L977">977</a><a id="L978" href="#L978">978</a><a id="L979" href="#L979">979</a><a id="L980" href="#L980">980</a><a id="L981" href="#L981">981</a><a id="L982" href="#L982">982</a><a id="L983" href="#L983">983</a><a id="L984" href="#L984">984</a><a id="L985" href="#L985">985</a><a id="L986" href="#L986">986</a><a id="L987" href="#L987">987</a><a id="L988" href="#L988">988</a><a id="L989" href="#L989">989</a><a id="L990" href="#L990">990</a><a id="L991" href="#L991">991</a><a id="L992" href="#L992">992</a><a id="L993" href="#L993">993</a><a id="L994" href="#L994">994</a><a id="L995" href="#L995">995</a><a id="L996" href="#L996">996</a><a id="L997" href="#L997">997</a><a id="L998" href="#L998">998</a><a id="L999" href="#L999">999</a><a id="L1000" href="#L1000">1000</a><a id="L1001" href="#L1001">1001</a><a id="L1002" href="#L1002">1002</a><a id="L1003" href="#L1003">1003</a><a id="L1004" href="#L1004">1004</a><a id="L1005" href="#L1005">1005</a><a id="L1006" href="#L1006">1006</a><a id="L1007" href="#L1007">1007</a><a id="L1008" href="#L1008">1008</a><a id="L1009" href="#L1009">1009</a><a id="L1010" href="#L1010">1010</a><a id="L1011" href="#L1011">1011</a><a id="L1012" href="#L1012">1012</a><a id="L1013" href="#L1013">1013</a><a id="L1014" href="#L1014">1014</a><a id="L1015" href="#L1015">1015</a><a id="L1016" href="#L1016">1016</a><a id="L1017" href="#L1017">1017</a><a id="L1018" href="#L1018">1018</a><a id="L1019" href="#L1019">1019</a><a id="L1020" href="#L1020">1020</a><a id="L1021" href="#L1021">1021</a><a id="L1022" href="#L1022">1022</a><a id="L1023" href="#L1023">1023</a><a id="L1024" href="#L1024">1024</a><a id="L1025" href="#L1025">1025</a><a id="L1026" href="#L1026">1026</a><a id="L1027" href="#L1027">1027</a><a id="L1028" href="#L1028">1028</a><a id="L1029" href="#L1029">1029</a><a id="L1030" href="#L1030">1030</a><a id="L1031" href="#L1031">1031</a><a id="L1032" href="#L1032">1032</a><a id="L1033" href="#L1033">1033</a><a id="L1034" href="#L1034">1034</a><a id="L1035" href="#L1035">1035</a><a id="L1036" href="#L1036">1036</a><a id="L1037" href="#L1037">1037</a><a id="L1038" href="#L1038">1038</a><a id="L1039" href="#L1039">1039</a><a id="L1040" href="#L1040">1040</a><a id="L1041" href="#L1041">1041</a><a id="L1042" href="#L1042">1042</a><a id="L1043" href="#L1043">1043</a><a id="L1044" href="#L1044">1044</a><a id="L1045" href="#L1045">1045</a><a id="L1046" href="#L1046">1046</a><a id="L1047" href="#L1047">1047</a><a id="L1048" href="#L1048">1048</a><a id="L1049" href="#L1049">1049</a><a id="L1050" href="#L1050">1050</a><a id="L1051" href="#L1051">1051</a><a id="L1052" href="#L1052">1052</a><a id="L1053" href="#L1053">1053</a><a id="L1054" href="#L1054">1054</a><a id="L1055" href="#L1055">1055</a><a id="L1056" href="#L1056">1056</a><a id="L1057" href="#L1057">1057</a><a id="L1058" href="#L1058">1058</a><a id="L1059" href="#L1059">1059</a><a id="L1060" href="#L1060">1060</a><a id="L1061" href="#L1061">1061</a><a id="L1062" href="#L1062">1062</a><a id="L1063" href="#L1063">1063</a><a id="L1064" href="#L1064">1064</a><a id="L1065" href="#L1065">1065</a><a id="L1066" href="#L1066">1066</a><a id="L1067" href="#L1067">1067</a><a id="L1068" href="#L1068">1068</a><a id="L1069" href="#L1069">1069</a><a id="L1070" href="#L1070">1070</a><a id="L1071" href="#L1071">1071</a><a id="L1072" href="#L1072">1072</a><a id="L1073" href="#L1073">1073</a><a id="L1074" href="#L1074">1074</a><a id="L1075" href="#L1075">1075</a><a id="L1076" href="#L1076">1076</a><a id="L1077" href="#L1077">1077</a><a id="L1078" href="#L1078">1078</a><a id="L1079" href="#L1079">1079</a><a id="L1080" href="#L1080">1080</a><a id="L1081" href="#L1081">1081</a><a id="L1082" href="#L1082">1082</a><a id="L1083" href="#L1083">1083</a><a id="L1084" href="#L1084">1084</a><a id="L1085" href="#L1085">1085</a><a id="L1086" href="#L1086">1086</a><a id="L1087" href="#L1087">1087</a><a id="L1088" href="#L1088">1088</a><a id="L1089" href="#L1089">1089</a><a id="L1090" href="#L1090">1090</a><a id="L1091" href="#L1091">1091</a><a id="L1092" href="#L1092">1092</a><a id="L1093" href="#L1093">1093</a><a id="L1094" href="#L1094">1094</a><a id="L1095" href="#L1095">1095</a><a id="L1096" href="#L1096">1096</a><a id="L1097" href="#L1097">1097</a><a id="L1098" href="#L1098">1098</a><a id="L1099" href="#L1099">1099</a><a id="L1100" href="#L1100">1100</a><a id="L1101" href="#L1101">1101</a><a id="L1102" href="#L1102">1102</a><a id="L1103" href="#L1103">1103</a><a id="L1104" href="#L1104">1104</a><a id="L1105" href="#L1105">1105</a><a id="L1106" href="#L1106">1106</a><a id="L1107" href="#L1107">1107</a><a id="L1108" href="#L1108">1108</a><a id="L1109" href="#L1109">1109</a><a id="L1110" href="#L1110">1110</a><a id="L1111" href="#L1111">1111</a><a id="L1112" href="#L1112">1112</a><a id="L1113" href="#L1113">1113</a><a id="L1114" href="#L1114">1114</a><a id="L1115" href="#L1115">1115</a><a id="L1116" href="#L1116">1116</a><a id="L1117" href="#L1117">1117</a><a id="L1118" href="#L1118">1118</a><a id="L1119" href="#L1119">1119</a><a id="L1120" href="#L1120">1120</a><a id="L1121" href="#L1121">1121</a><a id="L1122" href="#L1122">1122</a><a id="L1123" href="#L1123">1123</a><a id="L1124" href="#L1124">1124</a><a id="L1125" href="#L1125">1125</a><a id="L1126" href="#L1126">1126</a><a id="L1127" href="#L1127">1127</a><a id="L1128" href="#L1128">1128</a><a id="L1129" href="#L1129">1129</a><a id="L1130" href="#L1130">1130</a><a id="L1131" href="#L1131">1131</a><a id="L1132" href="#L1132">1132</a><a id="L1133" href="#L1133">1133</a><a id="L1134" href="#L1134">1134</a><a id="L1135" href="#L1135">1135</a><a id="L1136" href="#L1136">1136</a><a id="L1137" href="#L1137">1137</a><a id="L1138" href="#L1138">1138</a><a id="L1139" href="#L1139">1139</a><a id="L1140" href="#L1140">1140</a><a id="L1141" href="#L1141">1141</a><a id="L1142" href="#L1142">1142</a><a id="L1143" href="#L1143">1143</a><a id="L1144" href="#L1144">1144</a><a id="L1145" href="#L1145">1145</a><a id="L1146" href="#L1146">1146</a><a id="L1147" href="#L1147">1147</a><a id="L1148" href="#L1148">1148</a><a id="L1149" href="#L1149">1149</a><a id="L1150" href="#L1150">1150</a><a id="L1151" href="#L1151">1151</a><a id="L1152" href="#L1152">1152</a><a id="L1153" href="#L1153">1153</a><a id="L1154" href="#L1154">1154</a><a id="L1155" href="#L1155">1155</a><a id="L1156" href="#L1156">1156</a><a id="L1157" href="#L1157">1157</a><a id="L1158" href="#L1158">1158</a><a id="L1159" href="#L1159">1159</a><a id="L1160" href="#L1160">1160</a><a id="L1161" href="#L1161">1161</a><a id="L1162" href="#L1162">1162</a><a id="L1163" href="#L1163">1163</a><a id="L1164" href="#L1164">1164</a><a id="L1165" href="#L1165">1165</a><a id="L1166" href="#L1166">1166</a><a id="L1167" href="#L1167">1167</a><a id="L1168" href="#L1168">1168</a><a id="L1169" href="#L1169">1169</a><a id="L1170" href="#L1170">1170</a><a id="L1171" href="#L1171">1171</a><a id="L1172" href="#L1172">1172</a><a id="L1173" href="#L1173">1173</a><a id="L1174" href="#L1174">1174</a><a id="L1175" href="#L1175">1175</a><a id="L1176" href="#L1176">1176</a><a id="L1177" href="#L1177">1177</a><a id="L1178" href="#L1178">1178</a><a id="L1179" href="#L1179">1179</a><a id="L1180" href="#L1180">1180</a><a id="L1181" href="#L1181">1181</a><a id="L1182" href="#L1182">1182</a><a id="L1183" href="#L1183">1183</a><a id="L1184" href="#L1184">1184</a><a id="L1185" href="#L1185">1185</a><a id="L1186" href="#L1186">1186</a><a id="L1187" href="#L1187">1187</a><a id="L1188" href="#L1188">1188</a><a id="L1189" href="#L1189">1189</a><a id="L1190" href="#L1190">1190</a><a id="L1191" href="#L1191">1191</a><a id="L1192" href="#L1192">1192</a><a id="L1193" href="#L1193">1193</a><a id="L1194" href="#L1194">1194</a><a id="L1195" href="#L1195">1195</a><a id="L1196" href="#L1196">1196</a><a id="L1197" href="#L1197">1197</a><a id="L1198" href="#L1198">1198</a><a id="L1199" href="#L1199">1199</a><a id="L1200" href="#L1200">1200</a><a id="L1201" href="#L1201">1201</a><a id="L1202" href="#L1202">1202</a><a id="L1203" href="#L1203">1203</a><a id="L1204" href="#L1204">1204</a><a id="L1205" href="#L1205">1205</a><a id="L1206" href="#L1206">1206</a><a id="L1207" href="#L1207">1207</a><a id="L1208" href="#L1208">1208</a><a id="L1209" href="#L1209">1209</a><a id="L1210" href="#L1210">1210</a><a id="L1211" href="#L1211">1211</a><a id="L1212" href="#L1212">1212</a><a id="L1213" href="#L1213">1213</a><a id="L1214" href="#L1214">1214</a><a id="L1215" href="#L1215">1215</a><a id="L1216" href="#L1216">1216</a><a id="L1217" href="#L1217">1217</a><a id="L1218" href="#L1218">1218</a><a id="L1219" href="#L1219">1219</a><a id="L1220" href="#L1220">1220</a><a id="L1221" href="#L1221">1221</a><a id="L1222" href="#L1222">1222</a><a id="L1223" href="#L1223">1223</a><a id="L1224" href="#L1224">1224</a><a id="L1225" href="#L1225">1225</a><a id="L1226" href="#L1226">1226</a><a id="L1227" href="#L1227">1227</a><a id="L1228" href="#L1228">1228</a><a id="L1229" href="#L1229">1229</a><a id="L1230" href="#L1230">1230</a><a id="L1231" href="#L1231">1231</a><a id="L1232" href="#L1232">1232</a><a id="L1233" href="#L1233">1233</a><a id="L1234" href="#L1234">1234</a><a id="L1235" href="#L1235">1235</a><a id="L1236" href="#L1236">1236</a><a id="L1237" href="#L1237">1237</a><a id="L1238" href="#L1238">1238</a><a id="L1239" href="#L1239">1239</a><a id="L1240" href="#L1240">1240</a><a id="L1241" href="#L1241">1241</a><a id="L1242" href="#L1242">1242</a><a id="L1243" href="#L1243">1243</a><a id="L1244" href="#L1244">1244</a><a id="L1245" href="#L1245">1245</a><a id="L1246" href="#L1246">1246</a><a id="L1247" href="#L1247">1247</a><a id="L1248" href="#L1248">1248</a><a id="L1249" href="#L1249">1249</a><a id="L1250" href="#L1250">1250</a><a id="L1251" href="#L1251">1251</a><a id="L1252" href="#L1252">1252</a><a id="L1253" href="#L1253">1253</a><a id="L1254" href="#L1254">1254</a><a id="L1255" href="#L1255">1255</a><a id="L1256" href="#L1256">1256</a><a id="L1257" href="#L1257">1257</a><a id="L1258" href="#L1258">1258</a><a id="L1259" href="#L1259">1259</a><a id="L1260" href="#L1260">1260</a><a id="L1261" href="#L1261">1261</a><a id="L1262" href="#L1262">1262</a><a id="L1263" href="#L1263">1263</a><a id="L1264" href="#L1264">1264</a><a id="L1265" href="#L1265">1265</a><a id="L1266" href="#L1266">1266</a><a id="L1267" href="#L1267">1267</a><a id="L1268" href="#L1268">1268</a><a id="L1269" href="#L1269">1269</a><a id="L1270" href="#L1270">1270</a><a id="L1271" href="#L1271">1271</a><a id="L1272" href="#L1272">1272</a><a id="L1273" href="#L1273">1273</a><a id="L1274" href="#L1274">1274</a><a id="L1275" href="#L1275">1275</a><a id="L1276" href="#L1276">1276</a><a id="L1277" href="#L1277">1277</a><a id="L1278" href="#L1278">1278</a><a id="L1279" href="#L1279">1279</a><a id="L1280" href="#L1280">1280</a><a id="L1281" href="#L1281">1281</a><a id="L1282" href="#L1282">1282</a><a id="L1283" href="#L1283">1283</a><a id="L1284" href="#L1284">1284</a><a id="L1285" href="#L1285">1285</a><a id="L1286" href="#L1286">1286</a><a id="L1287" href="#L1287">1287</a><a id="L1288" href="#L1288">1288</a><a id="L1289" href="#L1289">1289</a><a id="L1290" href="#L1290">1290</a><a id="L1291" href="#L1291">1291</a><a id="L1292" href="#L1292">1292</a><a id="L1293" href="#L1293">1293</a><a id="L1294" href="#L1294">1294</a><a id="L1295" href="#L1295">1295</a><a id="L1296" href="#L1296">1296</a><a id="L1297" href="#L1297">1297</a><a id="L1298" href="#L1298">1298</a><a id="L1299" href="#L1299">1299</a><a id="L1300" href="#L1300">1300</a><a id="L1301" href="#L1301">1301</a><a id="L1302" href="#L1302">1302</a><a id="L1303" href="#L1303">1303</a><a id="L1304" href="#L1304">1304</a><a id="L1305" href="#L1305">1305</a><a id="L1306" href="#L1306">1306</a><a id="L1307" href="#L1307">1307</a><a id="L1308" href="#L1308">1308</a><a id="L1309" href="#L1309">1309</a><a id="L1310" href="#L1310">1310</a><a id="L1311" href="#L1311">1311</a><a id="L1312" href="#L1312">1312</a><a id="L1313" href="#L1313">1313</a><a id="L1314" href="#L1314">1314</a><a id="L1315" href="#L1315">1315</a><a id="L1316" href="#L1316">1316</a><a id="L1317" href="#L1317">1317</a><a id="L1318" href="#L1318">1318</a><a id="L1319" href="#L1319">1319</a><a id="L1320" href="#L1320">1320</a><a id="L1321" href="#L1321">1321</a><a id="L1322" href="#L1322">1322</a><a id="L1323" href="#L1323">1323</a><a id="L1324" href="#L1324">1324</a><a id="L1325" href="#L1325">1325</a><a id="L1326" href="#L1326">1326</a><a id="L1327" href="#L1327">1327</a><a id="L1328" href="#L1328">1328</a><a id="L1329" href="#L1329">1329</a><a id="L1330" href="#L1330">1330</a><a id="L1331" href="#L1331">1331</a><a id="L1332" href="#L1332">1332</a><a id="L1333" href="#L1333">1333</a><a id="L1334" href="#L1334">1334</a><a id="L1335" href="#L1335">1335</a><a id="L1336" href="#L1336">1336</a><a id="L1337" href="#L1337">1337</a><a id="L1338" href="#L1338">1338</a><a id="L1339" href="#L1339">1339</a><a id="L1340" href="#L1340">1340</a><a id="L1341" href="#L1341">1341</a><a id="L1342" href="#L1342">1342</a><a id="L1343" href="#L1343">1343</a><a id="L1344" href="#L1344">1344</a><a id="L1345" href="#L1345">1345</a><a id="L1346" href="#L1346">1346</a><a id="L1347" href="#L1347">1347</a><a id="L1348" href="#L1348">1348</a><a id="L1349" href="#L1349">1349</a><a id="L1350" href="#L1350">1350</a><a id="L1351" href="#L1351">1351</a><a id="L1352" href="#L1352">1352</a><a id="L1353" href="#L1353">1353</a><a id="L1354" href="#L1354">1354</a><a id="L1355" href="#L1355">1355</a><a id="L1356" href="#L1356">1356</a><a id="L1357" href="#L1357">1357</a><a id="L1358" href="#L1358">1358</a><a id="L1359" href="#L1359">1359</a><a id="L1360" href="#L1360">1360</a><a id="L1361" href="#L1361">1361</a><a id="L1362" href="#L1362">1362</a><a id="L1363" href="#L1363">1363</a><a id="L1364" href="#L1364">1364</a><a id="L1365" href="#L1365">1365</a><a id="L1366" href="#L1366">1366</a><a id="L1367" href="#L1367">1367</a><a id="L1368" href="#L1368">1368</a><a id="L1369" href="#L1369">1369</a><a id="L1370" href="#L1370">1370</a><a id="L1371" href="#L1371">1371</a><a id="L1372" href="#L1372">1372</a><a id="L1373" href="#L1373">1373</a><a id="L1374" href="#L1374">1374</a><a id="L1375" href="#L1375">1375</a><a id="L1376" href="#L1376">1376</a><a id="L1377" href="#L1377">1377</a><a id="L1378" href="#L1378">1378</a><a id="L1379" href="#L1379">1379</a><a id="L1380" href="#L1380">1380</a><a id="L1381" href="#L1381">1381</a><a id="L1382" href="#L1382">1382</a><a id="L1383" href="#L1383">1383</a><a id="L1384" href="#L1384">1384</a><a id="L1385" href="#L1385">1385</a><a id="L1386" href="#L1386">1386</a><a id="L1387" href="#L1387">1387</a><a id="L1388" href="#L1388">1388</a><a id="L1389" href="#L1389">1389</a><a id="L1390" href="#L1390">1390</a><a id="L1391" href="#L1391">1391</a><a id="L1392" href="#L1392">1392</a><a id="L1393" href="#L1393">1393</a><a id="L1394" href="#L1394">1394</a><a id="L1395" href="#L1395">1395</a><a id="L1396" href="#L1396">1396</a><a id="L1397" href="#L1397">1397</a><a id="L1398" href="#L1398">1398</a><a id="L1399" href="#L1399">1399</a><a id="L1400" href="#L1400">1400</a><a id="L1401" href="#L1401">1401</a><a id="L1402" href="#L1402">1402</a><a id="L1403" href="#L1403">1403</a><a id="L1404" href="#L1404">1404</a><a id="L1405" href="#L1405">1405</a><a id="L1406" href="#L1406">1406</a><a id="L1407" href="#L1407">1407</a><a id="L1408" href="#L1408">1408</a><a id="L1409" href="#L1409">1409</a><a id="L1410" href="#L1410">1410</a><a id="L1411" href="#L1411">1411</a><a id="L1412" href="#L1412">1412</a><a id="L1413" href="#L1413">1413</a><a id="L1414" href="#L1414">1414</a><a id="L1415" href="#L1415">1415</a><a id="L1416" href="#L1416">1416</a><a id="L1417" href="#L1417">1417</a><a id="L1418" href="#L1418">1418</a><a id="L1419" href="#L1419">1419</a><a id="L1420" href="#L1420">1420</a><a id="L1421" href="#L1421">1421</a><a id="L1422" href="#L1422">1422</a><a id="L1423" href="#L1423">1423</a><a id="L1424" href="#L1424">1424</a><a id="L1425" href="#L1425">1425</a><a id="L1426" href="#L1426">1426</a><a id="L1427" href="#L1427">1427</a><a id="L1428" href="#L1428">1428</a><a id="L1429" href="#L1429">1429</a><a id="L1430" href="#L1430">1430</a><a id="L1431" href="#L1431">1431</a><a id="L1432" href="#L1432">1432</a><a id="L1433" href="#L1433">1433</a><a id="L1434" href="#L1434">1434</a><a id="L1435" href="#L1435">1435</a><a id="L1436" href="#L1436">1436</a><a id="L1437" href="#L1437">1437</a><a id="L1438" href="#L1438">1438</a><a id="L1439" href="#L1439">1439</a><a id="L1440" href="#L1440">1440</a><a id="L1441" href="#L1441">1441</a><a id="L1442" href="#L1442">1442</a><a id="L1443" href="#L1443">1443</a><a id="L1444" href="#L1444">1444</a><a id="L1445" href="#L1445">1445</a><a id="L1446" href="#L1446">1446</a><a id="L1447" href="#L1447">1447</a><a id="L1448" href="#L1448">1448</a><a id="L1449" href="#L1449">1449</a><a id="L1450" href="#L1450">1450</a><a id="L1451" href="#L1451">1451</a><a id="L1452" href="#L1452">1452</a><a id="L1453" href="#L1453">1453</a><a id="L1454" href="#L1454">1454</a><a id="L1455" href="#L1455">1455</a><a id="L1456" href="#L1456">1456</a><a id="L1457" href="#L1457">1457</a><a id="L1458" href="#L1458">1458</a><a id="L1459" href="#L1459">1459</a><a id="L1460" href="#L1460">1460</a><a id="L1461" href="#L1461">1461</a><a id="L1462" href="#L1462">1462</a><a id="L1463" href="#L1463">1463</a><a id="L1464" href="#L1464">1464</a><a id="L1465" href="#L1465">1465</a><a id="L1466" href="#L1466">1466</a><a id="L1467" href="#L1467">1467</a><a id="L1468" href="#L1468">1468</a><a id="L1469" href="#L1469">1469</a><a id="L1470" href="#L1470">1470</a><a id="L1471" href="#L1471">1471</a><a id="L1472" href="#L1472">1472</a><a id="L1473" href="#L1473">1473</a><a id="L1474" href="#L1474">1474</a><a id="L1475" href="#L1475">1475</a><a id="L1476" href="#L1476">1476</a><a id="L1477" href="#L1477">1477</a><a id="L1478" href="#L1478">1478</a><a id="L1479" href="#L1479">1479</a><a id="L1480" href="#L1480">1480</a><a id="L1481" href="#L1481">1481</a><a id="L1482" href="#L1482">1482</a><a id="L1483" href="#L1483">1483</a><a id="L1484" href="#L1484">1484</a><a id="L1485" href="#L1485">1485</a><a id="L1486" href="#L1486">1486</a><a id="L1487" href="#L1487">1487</a><a id="L1488" href="#L1488">1488</a><a id="L1489" href="#L1489">1489</a><a id="L1490" href="#L1490">1490</a><a id="L1491" href="#L1491">1491</a><a id="L1492" href="#L1492">1492</a><a id="L1493" href="#L1493">1493</a><a id="L1494" href="#L1494">1494</a><a id="L1495" href="#L1495">1495</a><a id="L1496" href="#L1496">1496</a><a id="L1497" href="#L1497">1497</a><a id="L1498" href="#L1498">1498</a><a id="L1499" href="#L1499">1499</a><a id="L1500" href="#L1500">1500</a><a id="L1501" href="#L1501">1501</a><a id="L1502" href="#L1502">1502</a><a id="L1503" href="#L1503">1503</a><a id="L1504" href="#L1504">1504</a><a id="L1505" href="#L1505">1505</a><a id="L1506" href="#L1506">1506</a><a id="L1507" href="#L1507">1507</a><a id="L1508" href="#L1508">1508</a><a id="L1509" href="#L1509">1509</a><a id="L1510" href="#L1510">1510</a><a id="L1511" href="#L1511">1511</a><a id="L1512" href="#L1512">1512</a><a id="L1513" href="#L1513">1513</a><a id="L1514" href="#L1514">1514</a><a id="L1515" href="#L1515">1515</a><a id="L1516" href="#L1516">1516</a><a id="L1517" href="#L1517">1517</a><a id="L1518" href="#L1518">1518</a><a id="L1519" href="#L1519">1519</a><a id="L1520" href="#L1520">1520</a><a id="L1521" href="#L1521">1521</a><a id="L1522" href="#L1522">1522</a><a id="L1523" href="#L1523">1523</a><a id="L1524" href="#L1524">1524</a><a id="L1525" href="#L1525">1525</a><a id="L1526" href="#L1526">1526</a><a id="L1527" href="#L1527">1527</a><a id="L1528" href="#L1528">1528</a><a id="L1529" href="#L1529">1529</a><a id="L1530" href="#L1530">1530</a><a id="L1531" href="#L1531">1531</a><a id="L1532" href="#L1532">1532</a><a id="L1533" href="#L1533">1533</a><a id="L1534" href="#L1534">1534</a><a id="L1535" href="#L1535">1535</a><a id="L1536" href="#L1536">1536</a><a id="L1537" href="#L1537">1537</a><a id="L1538" href="#L1538">1538</a><a id="L1539" href="#L1539">1539</a><a id="L1540" href="#L1540">1540</a><a id="L1541" href="#L1541">1541</a><a id="L1542" href="#L1542">1542</a><a id="L1543" href="#L1543">1543</a><a id="L1544" href="#L1544">1544</a><a id="L1545" href="#L1545">1545</a><a id="L1546" href="#L1546">1546</a><a id="L1547" href="#L1547">1547</a><a id="L1548" href="#L1548">1548</a><a id="L1549" href="#L1549">1549</a><a id="L1550" href="#L1550">1550</a><a id="L1551" href="#L1551">1551</a><a id="L1552" href="#L1552">1552</a><a id="L1553" href="#L1553">1553</a><a id="L1554" href="#L1554">1554</a><a id="L1555" href="#L1555">1555</a><a id="L1556" href="#L1556">1556</a><a id="L1557" href="#L1557">1557</a><a id="L1558" href="#L1558">1558</a><a id="L1559" href="#L1559">1559</a><a id="L1560" href="#L1560">1560</a><a id="L1561" href="#L1561">1561</a><a id="L1562" href="#L1562">1562</a><a id="L1563" href="#L1563">1563</a><a id="L1564" href="#L1564">1564</a><a id="L1565" href="#L1565">1565</a><a id="L1566" href="#L1566">1566</a><a id="L1567" href="#L1567">1567</a><a id="L1568" href="#L1568">1568</a><a id="L1569" href="#L1569">1569</a><a id="L1570" href="#L1570">1570</a><a id="L1571" href="#L1571">1571</a><a id="L1572" href="#L1572">1572</a><a id="L1573" href="#L1573">1573</a><a id="L1574" href="#L1574">1574</a><a id="L1575" href="#L1575">1575</a><a id="L1576" href="#L1576">1576</a><a id="L1577" href="#L1577">1577</a><a id="L1578" href="#L1578">1578</a><a id="L1579" href="#L1579">1579</a><a id="L1580" href="#L1580">1580</a><a id="L1581" href="#L1581">1581</a><a id="L1582" href="#L1582">1582</a><a id="L1583" href="#L1583">1583</a><a id="L1584" href="#L1584">1584</a><a id="L1585" href="#L1585">1585</a><a id="L1586" href="#L1586">1586</a><a id="L1587" href="#L1587">1587</a><a id="L1588" href="#L1588">1588</a><a id="L1589" href="#L1589">1589</a><a id="L1590" href="#L1590">1590</a><a id="L1591" href="#L1591">1591</a><a id="L1592" href="#L1592">1592</a><a id="L1593" href="#L1593">1593</a><a id="L1594" href="#L1594">1594</a><a id="L1595" href="#L1595">1595</a><a id="L1596" href="#L1596">1596</a><a id="L1597" href="#L1597">1597</a><a id="L1598" href="#L1598">1598</a><a id="L1599" href="#L1599">1599</a><a id="L1600" href="#L1600">1600</a><a id="L1601" href="#L1601">1601</a><a id="L1602" href="#L1602">1602</a><a id="L1603" href="#L1603">1603</a><a id="L1604" href="#L1604">1604</a><a id="L1605" href="#L1605">1605</a><a id="L1606" href="#L1606">1606</a><a id="L1607" href="#L1607">1607</a><a id="L1608" href="#L1608">1608</a><a id="L1609" href="#L1609">1609</a><a id="L1610" href="#L1610">1610</a><a id="L1611" href="#L1611">1611</a><a id="L1612" href="#L1612">1612</a><a id="L1613" href="#L1613">1613</a><a id="L1614" href="#L1614">1614</a><a id="L1615" href="#L1615">1615</a><a id="L1616" href="#L1616">1616</a><a id="L1617" href="#L1617">1617</a><a id="L1618" href="#L1618">1618</a><a id="L1619" href="#L1619">1619</a><a id="L1620" href="#L1620">1620</a><a id="L1621" href="#L1621">1621</a><a id="L1622" href="#L1622">1622</a><a id="L1623" href="#L1623">1623</a><a id="L1624" href="#L1624">1624</a><a id="L1625" href="#L1625">1625</a><a id="L1626" href="#L1626">1626</a><a id="L1627" href="#L1627">1627</a><a id="L1628" href="#L1628">1628</a><a id="L1629" href="#L1629">1629</a><a id="L1630" href="#L1630">1630</a><a id="L1631" href="#L1631">1631</a><a id="L1632" href="#L1632">1632</a><a id="L1633" href="#L1633">1633</a><a id="L1634" href="#L1634">1634</a><a id="L1635" href="#L1635">1635</a><a id="L1636" href="#L1636">1636</a><a id="L1637" href="#L1637">1637</a><a id="L1638" href="#L1638">1638</a><a id="L1639" href="#L1639">1639</a><a id="L1640" href="#L1640">1640</a><a id="L1641" href="#L1641">1641</a><a id="L1642" href="#L1642">1642</a><a id="L1643" href="#L1643">1643</a><a id="L1644" href="#L1644">1644</a><a id="L1645" href="#L1645">1645</a><a id="L1646" href="#L1646">1646</a><a id="L1647" href="#L1647">1647</a><a id="L1648" href="#L1648">1648</a><a id="L1649" href="#L1649">1649</a><a id="L1650" href="#L1650">1650</a><a id="L1651" href="#L1651">1651</a><a id="L1652" href="#L1652">1652</a><a id="L1653" href="#L1653">1653</a><a id="L1654" href="#L1654">1654</a><a id="L1655" href="#L1655">1655</a><a id="L1656" href="#L1656">1656</a><a id="L1657" href="#L1657">1657</a><a id="L1658" href="#L1658">1658</a><a id="L1659" href="#L1659">1659</a><a id="L1660" href="#L1660">1660</a><a id="L1661" href="#L1661">1661</a><a id="L1662" href="#L1662">1662</a><a id="L1663" href="#L1663">1663</a><a id="L1664" href="#L1664">1664</a><a id="L1665" href="#L1665">1665</a><a id="L1666" href="#L1666">1666</a><a id="L1667" href="#L1667">1667</a><a id="L1668" href="#L1668">1668</a><a id="L1669" href="#L1669">1669</a><a id="L1670" href="#L1670">1670</a><a id="L1671" href="#L1671">1671</a><a id="L1672" href="#L1672">1672</a><a id="L1673" href="#L1673">1673</a><a id="L1674" href="#L1674">1674</a><a id="L1675" href="#L1675">1675</a><a id="L1676" href="#L1676">1676</a><a id="L1677" href="#L1677">1677</a><a id="L1678" href="#L1678">1678</a><a id="L1679" href="#L1679">1679</a><a id="L1680" href="#L1680">1680</a><a id="L1681" href="#L1681">1681</a><a id="L1682" href="#L1682">1682</a><a id="L1683" href="#L1683">1683</a><a id="L1684" href="#L1684">1684</a><a id="L1685" href="#L1685">1685</a><a id="L1686" href="#L1686">1686</a><a id="L1687" href="#L1687">1687</a><a id="L1688" href="#L1688">1688</a><a id="L1689" href="#L1689">1689</a><a id="L1690" href="#L1690">1690</a><a id="L1691" href="#L1691">1691</a><a id="L1692" href="#L1692">1692</a><a id="L1693" href="#L1693">1693</a><a id="L1694" href="#L1694">1694</a><a id="L1695" href="#L1695">1695</a><a id="L1696" href="#L1696">1696</a><a id="L1697" href="#L1697">1697</a><a id="L1698" href="#L1698">1698</a><a id="L1699" href="#L1699">1699</a><a id="L1700" href="#L1700">1700</a><a id="L1701" href="#L1701">1701</a><a id="L1702" href="#L1702">1702</a><a id="L1703" href="#L1703">1703</a><a id="L1704" href="#L1704">1704</a><a id="L1705" href="#L1705">1705</a><a id="L1706" href="#L1706">1706</a><a id="L1707" href="#L1707">1707</a><a id="L1708" href="#L1708">1708</a><a id="L1709" href="#L1709">1709</a><a id="L1710" href="#L1710">1710</a><a id="L1711" href="#L1711">1711</a><a id="L1712" href="#L1712">1712</a><a id="L1713" href="#L1713">1713</a><a id="L1714" href="#L1714">1714</a><a id="L1715" href="#L1715">1715</a><a id="L1716" href="#L1716">1716</a><a id="L1717" href="#L1717">1717</a><a id="L1718" href="#L1718">1718</a><a id="L1719" href="#L1719">1719</a><a id="L1720" href="#L1720">1720</a><a id="L1721" href="#L1721">1721</a><a id="L1722" href="#L1722">1722</a><a id="L1723" href="#L1723">1723</a><a id="L1724" href="#L1724">1724</a><a id="L1725" href="#L1725">1725</a><a id="L1726" href="#L1726">1726</a><a id="L1727" href="#L1727">1727</a><a id="L1728" href="#L1728">1728</a><a id="L1729" href="#L1729">1729</a><a id="L1730" href="#L1730">1730</a><a id="L1731" href="#L1731">1731</a><a id="L1732" href="#L1732">1732</a><a id="L1733" href="#L1733">1733</a><a id="L1734" href="#L1734">1734</a><a id="L1735" href="#L1735">1735</a><a id="L1736" href="#L1736">1736</a><a id="L1737" href="#L1737">1737</a><a id="L1738" href="#L1738">1738</a><a id="L1739" href="#L1739">1739</a><a id="L1740" href="#L1740">1740</a><a id="L1741" href="#L1741">1741</a><a id="L1742" href="#L1742">1742</a><a id="L1743" href="#L1743">1743</a><a id="L1744" href="#L1744">1744</a><a id="L1745" href="#L1745">1745</a><a id="L1746" href="#L1746">1746</a><a id="L1747" href="#L1747">1747</a><a id="L1748" href="#L1748">1748</a><a id="L1749" href="#L1749">1749</a><a id="L1750" href="#L1750">1750</a><a id="L1751" href="#L1751">1751</a><a id="L1752" href="#L1752">1752</a><a id="L1753" href="#L1753">1753</a><a id="L1754" href="#L1754">1754</a><a id="L1755" href="#L1755">1755</a><a id="L1756" href="#L1756">1756</a><a id="L1757" href="#L1757">1757</a><a id="L1758" href="#L1758">1758</a><a id="L1759" href="#L1759">1759</a><a id="L1760" href="#L1760">1760</a><a id="L1761" href="#L1761">1761</a><a id="L1762" href="#L1762">1762</a><a id="L1763" href="#L1763">1763</a><a id="L1764" href="#L1764">1764</a><a id="L1765" href="#L1765">1765</a><a id="L1766" href="#L1766">1766</a><a id="L1767" href="#L1767">1767</a><a id="L1768" href="#L1768">1768</a><a id="L1769" href="#L1769">1769</a><a id="L1770" href="#L1770">1770</a><a id="L1771" href="#L1771">1771</a><a id="L1772" href="#L1772">1772</a><a id="L1773" href="#L1773">1773</a><a id="L1774" href="#L1774">1774</a><a id="L1775" href="#L1775">1775</a><a id="L1776" href="#L1776">1776</a><a id="L1777" href="#L1777">1777</a><a id="L1778" href="#L1778">1778</a><a id="L1779" href="#L1779">1779</a><a id="L1780" href="#L1780">1780</a><a id="L1781" href="#L1781">1781</a><a id="L1782" href="#L1782">1782</a><a id="L1783" href="#L1783">1783</a><a id="L1784" href="#L1784">1784</a><a id="L1785" href="#L1785">1785</a><a id="L1786" href="#L1786">1786</a><a id="L1787" href="#L1787">1787</a><a id="L1788" href="#L1788">1788</a><a id="L1789" href="#L1789">1789</a><a id="L1790" href="#L1790">1790</a><a id="L1791" href="#L1791">1791</a><a id="L1792" href="#L1792">1792</a><a id="L1793" href="#L1793">1793</a><a id="L1794" href="#L1794">1794</a><a id="L1795" href="#L1795">1795</a><a id="L1796" href="#L1796">1796</a><a id="L1797" href="#L1797">1797</a><a id="L1798" href="#L1798">1798</a><a id="L1799" href="#L1799">1799</a><a id="L1800" href="#L1800">1800</a><a id="L1801" href="#L1801">1801</a><a id="L1802" href="#L1802">1802</a><a id="L1803" href="#L1803">1803</a><a id="L1804" href="#L1804">1804</a><a id="L1805" href="#L1805">1805</a><a id="L1806" href="#L1806">1806</a><a id="L1807" href="#L1807">1807</a><a id="L1808" href="#L1808">1808</a><a id="L1809" href="#L1809">1809</a><a id="L1810" href="#L1810">1810</a><a id="L1811" href="#L1811">1811</a><a id="L1812" href="#L1812">1812</a><a id="L1813" href="#L1813">1813</a><a id="L1814" href="#L1814">1814</a><a id="L1815" href="#L1815">1815</a><a id="L1816" href="#L1816">1816</a><a id="L1817" href="#L1817">1817</a><a id="L1818" href="#L1818">1818</a><a id="L1819" href="#L1819">1819</a><a id="L1820" href="#L1820">1820</a><a id="L1821" href="#L1821">1821</a><a id="L1822" href="#L1822">1822</a><a id="L1823" href="#L1823">1823</a><a id="L1824" href="#L1824">1824</a><a id="L1825" href="#L1825">1825</a><a id="L1826" href="#L1826">1826</a><a id="L1827" href="#L1827">1827</a><a id="L1828" href="#L1828">1828</a><a id="L1829" href="#L1829">1829</a><a id="L1830" href="#L1830">1830</a><a id="L1831" href="#L1831">1831</a><a id="L1832" href="#L1832">1832</a><a id="L1833" href="#L1833">1833</a><a id="L1834" href="#L1834">1834</a><a id="L1835" href="#L1835">1835</a><a id="L1836" href="#L1836">1836</a><a id="L1837" href="#L1837">1837</a><a id="L1838" href="#L1838">1838</a><a id="L1839" href="#L1839">1839</a><a id="L1840" href="#L1840">1840</a><a id="L1841" href="#L1841">1841</a><a id="L1842" href="#L1842">1842</a><a id="L1843" href="#L1843">1843</a><a id="L1844" href="#L1844">1844</a><a id="L1845" href="#L1845">1845</a><a id="L1846" href="#L1846">1846</a><a id="L1847" href="#L1847">1847</a><a id="L1848" href="#L1848">1848</a><a id="L1849" href="#L1849">1849</a><a id="L1850" href="#L1850">1850</a><a id="L1851" href="#L1851">1851</a><a id="L1852" href="#L1852">1852</a><a id="L1853" href="#L1853">1853</a><a id="L1854" href="#L1854">1854</a><a id="L1855" href="#L1855">1855</a><a id="L1856" href="#L1856">1856</a><a id="L1857" href="#L1857">1857</a><a id="L1858" href="#L1858">1858</a><a id="L1859" href="#L1859">1859</a><a id="L1860" href="#L1860">1860</a><a id="L1861" href="#L1861">1861</a><a id="L1862" href="#L1862">1862</a><a id="L1863" href="#L1863">1863</a><a id="L1864" href="#L1864">1864</a><a id="L1865" href="#L1865">1865</a><a id="L1866" href="#L1866">1866</a><a id="L1867" href="#L1867">1867</a><a id="L1868" href="#L1868">1868</a><a id="L1869" href="#L1869">1869</a><a id="L1870" href="#L1870">1870</a><a id="L1871" href="#L1871">1871</a><a id="L1872" href="#L1872">1872</a><a id="L1873" href="#L1873">1873</a><a id="L1874" href="#L1874">1874</a><a id="L1875" href="#L1875">1875</a><a id="L1876" href="#L1876">1876</a><a id="L1877" href="#L1877">1877</a><a id="L1878" href="#L1878">1878</a><a id="L1879" href="#L1879">1879</a><a id="L1880" href="#L1880">1880</a><a id="L1881" href="#L1881">1881</a><a id="L1882" href="#L1882">1882</a><a id="L1883" href="#L1883">1883</a><a id="L1884" href="#L1884">1884</a><a id="L1885" href="#L1885">1885</a><a id="L1886" href="#L1886">1886</a><a id="L1887" href="#L1887">1887</a><a id="L1888" href="#L1888">1888</a><a id="L1889" href="#L1889">1889</a><a id="L1890" href="#L1890">1890</a><a id="L1891" href="#L1891">1891</a><a id="L1892" href="#L1892">1892</a><a id="L1893" href="#L1893">1893</a><a id="L1894" href="#L1894">1894</a><a id="L1895" href="#L1895">1895</a><a id="L1896" href="#L1896">1896</a><a id="L1897" href="#L1897">1897</a><a id="L1898" href="#L1898">1898</a><a id="L1899" href="#L1899">1899</a><a id="L1900" href="#L1900">1900</a><a id="L1901" href="#L1901">1901</a><a id="L1902" href="#L1902">1902</a><a id="L1903" href="#L1903">1903</a><a id="L1904" href="#L1904">1904</a><a id="L1905" href="#L1905">1905</a><a id="L1906" href="#L1906">1906</a><a id="L1907" href="#L1907">1907</a><a id="L1908" href="#L1908">1908</a><a id="L1909" href="#L1909">1909</a><a id="L1910" href="#L1910">1910</a><a id="L1911" href="#L1911">1911</a><a id="L1912" href="#L1912">1912</a><a id="L1913" href="#L1913">1913</a><a id="L1914" href="#L1914">1914</a><a id="L1915" href="#L1915">1915</a><a id="L1916" href="#L1916">1916</a><a id="L1917" href="#L1917">1917</a><a id="L1918" href="#L1918">1918</a><a id="L1919" href="#L1919">1919</a><a id="L1920" href="#L1920">1920</a><a id="L1921" href="#L1921">1921</a><a id="L1922" href="#L1922">1922</a><a id="L1923" href="#L1923">1923</a><a id="L1924" href="#L1924">1924</a><a id="L1925" href="#L1925">1925</a><a id="L1926" href="#L1926">1926</a><a id="L1927" href="#L1927">1927</a><a id="L1928" href="#L1928">1928</a><a id="L1929" href="#L1929">1929</a><a id="L1930" href="#L1930">1930</a><a id="L1931" href="#L1931">1931</a><a id="L1932" href="#L1932">1932</a><a id="L1933" href="#L1933">1933</a><a id="L1934" href="#L1934">1934</a><a id="L1935" href="#L1935">1935</a><a id="L1936" href="#L1936">1936</a><a id="L1937" href="#L1937">1937</a><a id="L1938" href="#L1938">1938</a><a id="L1939" href="#L1939">1939</a><a id="L1940" href="#L1940">1940</a><a id="L1941" href="#L1941">1941</a><a id="L1942" href="#L1942">1942</a><a id="L1943" href="#L1943">1943</a><a id="L1944" href="#L1944">1944</a><a id="L1945" href="#L1945">1945</a><a id="L1946" href="#L1946">1946</a><a id="L1947" href="#L1947">1947</a><a id="L1948" href="#L1948">1948</a><a id="L1949" href="#L1949">1949</a><a id="L1950" href="#L1950">1950</a><a id="L1951" href="#L1951">1951</a><a id="L1952" href="#L1952">1952</a><a id="L1953" href="#L1953">1953</a><a id="L1954" href="#L1954">1954</a><a id="L1955" href="#L1955">1955</a><a id="L1956" href="#L1956">1956</a><a id="L1957" href="#L1957">1957</a><a id="L1958" href="#L1958">1958</a><a id="L1959" href="#L1959">1959</a><a id="L1960" href="#L1960">1960</a><a id="L1961" href="#L1961">1961</a><a id="L1962" href="#L1962">1962</a><a id="L1963" href="#L1963">1963</a><a id="L1964" href="#L1964">1964</a><a id="L1965" href="#L1965">1965</a><a id="L1966" href="#L1966">1966</a><a id="L1967" href="#L1967">1967</a><a id="L1968" href="#L1968">1968</a><a id="L1969" href="#L1969">1969</a><a id="L1970" href="#L1970">1970</a><a id="L1971" href="#L1971">1971</a><a id="L1972" href="#L1972">1972</a><a id="L1973" href="#L1973">1973</a><a id="L1974" href="#L1974">1974</a><a id="L1975" href="#L1975">1975</a><a id="L1976" href="#L1976">1976</a><a id="L1977" href="#L1977">1977</a><a id="L1978" href="#L1978">1978</a><a id="L1979" href="#L1979">1979</a><a id="L1980" href="#L1980">1980</a><a id="L1981" href="#L1981">1981</a><a id="L1982" href="#L1982">1982</a><a id="L1983" href="#L1983">1983</a><a id="L1984" href="#L1984">1984</a><a id="L1985" href="#L1985">1985</a><a id="L1986" href="#L1986">1986</a><a id="L1987" href="#L1987">1987</a><a id="L1988" href="#L1988">1988</a><a id="L1989" href="#L1989">1989</a><a id="L1990" href="#L1990">1990</a><a id="L1991" href="#L1991">1991</a><a id="L1992" href="#L1992">1992</a><a id="L1993" href="#L1993">1993</a><a id="L1994" href="#L1994">1994</a><a id="L1995" href="#L1995">1995</a><a id="L1996" href="#L1996">1996</a><a id="L1997" href="#L1997">1997</a><a id="L1998" href="#L1998">1998</a><a id="L1999" href="#L1999">1999</a><a id="L2000" href="#L2000">2000</a><a id="L2001" href="#L2001">2001</a><a id="L2002" href="#L2002">2002</a><a id="L2003" href="#L2003">2003</a><a id="L2004" href="#L2004">2004</a><a id="L2005" href="#L2005">2005</a><a id="L2006" href="#L2006">2006</a><a id="L2007" href="#L2007">2007</a><a id="L2008" href="#L2008">2008</a><a id="L2009" href="#L2009">2009</a><a id="L2010" href="#L2010">2010</a><a id="L2011" href="#L2011">2011</a><a id="L2012" href="#L2012">2012</a><a id="L2013" href="#L2013">2013</a><a id="L2014" href="#L2014">2014</a><a id="L2015" href="#L2015">2015</a><a id="L2016" href="#L2016">2016</a><a id="L2017" href="#L2017">2017</a><a id="L2018" href="#L2018">2018</a><a id="L2019" href="#L2019">2019</a><a id="L2020" href="#L2020">2020</a><a id="L2021" href="#L2021">2021</a><a id="L2022" href="#L2022">2022</a><a id="L2023" href="#L2023">2023</a><a id="L2024" href="#L2024">2024</a><a id="L2025" href="#L2025">2025</a><a id="L2026" href="#L2026">2026</a><a id="L2027" href="#L2027">2027</a><a id="L2028" href="#L2028">2028</a><a id="L2029" href="#L2029">2029</a><a id="L2030" href="#L2030">2030</a><a id="L2031" href="#L2031">2031</a><a id="L2032" href="#L2032">2032</a><a id="L2033" href="#L2033">2033</a><a id="L2034" href="#L2034">2034</a><a id="L2035" href="#L2035">2035</a><a id="L2036" href="#L2036">2036</a><a id="L2037" href="#L2037">2037</a><a id="L2038" href="#L2038">2038</a><a id="L2039" href="#L2039">2039</a><a id="L2040" href="#L2040">2040</a><a id="L2041" href="#L2041">2041</a><a id="L2042" href="#L2042">2042</a><a id="L2043" href="#L2043">2043</a><a id="L2044" href="#L2044">2044</a><a id="L2045" href="#L2045">2045</a><a id="L2046" href="#L2046">2046</a><a id="L2047" href="#L2047">2047</a><a id="L2048" href="#L2048">2048</a><a id="L2049" href="#L2049">2049</a><a id="L2050" href="#L2050">2050</a><a id="L2051" href="#L2051">2051</a><a id="L2052" href="#L2052">2052</a><a id="L2053" href="#L2053">2053</a><a id="L2054" href="#L2054">2054</a><a id="L2055" href="#L2055">2055</a><a id="L2056" href="#L2056">2056</a><a id="L2057" href="#L2057">2057</a><a id="L2058" href="#L2058">2058</a><a id="L2059" href="#L2059">2059</a><a id="L2060" href="#L2060">2060</a><a id="L2061" href="#L2061">2061</a><a id="L2062" href="#L2062">2062</a><a id="L2063" href="#L2063">2063</a><a id="L2064" href="#L2064">2064</a><a id="L2065" href="#L2065">2065</a><a id="L2066" href="#L2066">2066</a><a id="L2067" href="#L2067">2067</a><a id="L2068" href="#L2068">2068</a><a id="L2069" href="#L2069">2069</a><a id="L2070" href="#L2070">2070</a><a id="L2071" href="#L2071">2071</a><a id="L2072" href="#L2072">2072</a><a id="L2073" href="#L2073">2073</a><a id="L2074" href="#L2074">2074</a><a id="L2075" href="#L2075">2075</a><a id="L2076" href="#L2076">2076</a><a id="L2077" href="#L2077">2077</a><a id="L2078" href="#L2078">2078</a><a id="L2079" href="#L2079">2079</a><a id="L2080" href="#L2080">2080</a><a id="L2081" href="#L2081">2081</a><a id="L2082" href="#L2082">2082</a><a id="L2083" href="#L2083">2083</a><a id="L2084" href="#L2084">2084</a><a id="L2085" href="#L2085">2085</a><a id="L2086" href="#L2086">2086</a><a id="L2087" href="#L2087">2087</a><a id="L2088" href="#L2088">2088</a><a id="L2089" href="#L2089">2089</a><a id="L2090" href="#L2090">2090</a><a id="L2091" href="#L2091">2091</a><a id="L2092" href="#L2092">2092</a><a id="L2093" href="#L2093">2093</a><a id="L2094" href="#L2094">2094</a><a id="L2095" href="#L2095">2095</a><a id="L2096" href="#L2096">2096</a><a id="L2097" href="#L2097">2097</a><a id="L2098" href="#L2098">2098</a><a id="L2099" href="#L2099">2099</a><a id="L2100" href="#L2100">2100</a><a id="L2101" href="#L2101">2101</a><a id="L2102" href="#L2102">2102</a><a id="L2103" href="#L2103">2103</a><a id="L2104" href="#L2104">2104</a><a id="L2105" href="#L2105">2105</a><a id="L2106" href="#L2106">2106</a><a id="L2107" href="#L2107">2107</a><a id="L2108" href="#L2108">2108</a><a id="L2109" href="#L2109">2109</a><a id="L2110" href="#L2110">2110</a><a id="L2111" href="#L2111">2111</a><a id="L2112" href="#L2112">2112</a><a id="L2113" href="#L2113">2113</a><a id="L2114" href="#L2114">2114</a><a id="L2115" href="#L2115">2115</a><a id="L2116" href="#L2116">2116</a><a id="L2117" href="#L2117">2117</a><a id="L2118" href="#L2118">2118</a><a id="L2119" href="#L2119">2119</a><a id="L2120" href="#L2120">2120</a><a id="L2121" href="#L2121">2121</a><a id="L2122" href="#L2122">2122</a><a id="L2123" href="#L2123">2123</a><a id="L2124" href="#L2124">2124</a><a id="L2125" href="#L2125">2125</a><a id="L2126" href="#L2126">2126</a><a id="L2127" href="#L2127">2127</a><a id="L2128" href="#L2128">2128</a><a id="L2129" href="#L2129">2129</a><a id="L2130" href="#L2130">2130</a><a id="L2131" href="#L2131">2131</a><a id="L2132" href="#L2132">2132</a><a id="L2133" href="#L2133">2133</a><a id="L2134" href="#L2134">2134</a><a id="L2135" href="#L2135">2135</a><a id="L2136" href="#L2136">2136</a><a id="L2137" href="#L2137">2137</a><a id="L2138" href="#L2138">2138</a><a id="L2139" href="#L2139">2139</a><a id="L2140" href="#L2140">2140</a><a id="L2141" href="#L2141">2141</a><a id="L2142" href="#L2142">2142</a><a id="L2143" href="#L2143">2143</a><a id="L2144" href="#L2144">2144</a><a id="L2145" href="#L2145">2145</a><a id="L2146" href="#L2146">2146</a><a id="L2147" href="#L2147">2147</a><a id="L2148" href="#L2148">2148</a><a id="L2149" href="#L2149">2149</a><a id="L2150" href="#L2150">2150</a><a id="L2151" href="#L2151">2151</a><a id="L2152" href="#L2152">2152</a><a id="L2153" href="#L2153">2153</a><a id="L2154" href="#L2154">2154</a><a id="L2155" href="#L2155">2155</a><a id="L2156" href="#L2156">2156</a><a id="L2157" href="#L2157">2157</a><a id="L2158" href="#L2158">2158</a><a id="L2159" href="#L2159">2159</a><a id="L2160" href="#L2160">2160</a><a id="L2161" href="#L2161">2161</a><a id="L2162" href="#L2162">2162</a><a id="L2163" href="#L2163">2163</a><a id="L2164" href="#L2164">2164</a><a id="L2165" href="#L2165">2165</a><a id="L2166" href="#L2166">2166</a><a id="L2167" href="#L2167">2167</a><a id="L2168" href="#L2168">2168</a><a id="L2169" href="#L2169">2169</a><a id="L2170" href="#L2170">2170</a><a id="L2171" href="#L2171">2171</a><a id="L2172" href="#L2172">2172</a><a id="L2173" href="#L2173">2173</a><a id="L2174" href="#L2174">2174</a><a id="L2175" href="#L2175">2175</a><a id="L2176" href="#L2176">2176</a><a id="L2177" href="#L2177">2177</a><a id="L2178" href="#L2178">2178</a><a id="L2179" href="#L2179">2179</a><a id="L2180" href="#L2180">2180</a><a id="L2181" href="#L2181">2181</a><a id="L2182" href="#L2182">2182</a><a id="L2183" href="#L2183">2183</a><a id="L2184" href="#L2184">2184</a><a id="L2185" href="#L2185">2185</a><a id="L2186" href="#L2186">2186</a><a id="L2187" href="#L2187">2187</a><a id="L2188" href="#L2188">2188</a><a id="L2189" href="#L2189">2189</a><a id="L2190" href="#L2190">2190</a><a id="L2191" href="#L2191">2191</a><a id="L2192" href="#L2192">2192</a><a id="L2193" href="#L2193">2193</a><a id="L2194" href="#L2194">2194</a><a id="L2195" href="#L2195">2195</a><a id="L2196" href="#L2196">2196</a><a id="L2197" href="#L2197">2197</a><a id="L2198" href="#L2198">2198</a><a id="L2199" href="#L2199">2199</a><a id="L2200" href="#L2200">2200</a><a id="L2201" href="#L2201">2201</a><a id="L2202" href="#L2202">2202</a><a id="L2203" href="#L2203">2203</a><a id="L2204" href="#L2204">2204</a><a id="L2205" href="#L2205">2205</a><a id="L2206" href="#L2206">2206</a><a id="L2207" href="#L2207">2207</a><a id="L2208" href="#L2208">2208</a><a id="L2209" href="#L2209">2209</a><a id="L2210" href="#L2210">2210</a><a id="L2211" href="#L2211">2211</a><a id="L2212" href="#L2212">2212</a><a id="L2213" href="#L2213">2213</a><a id="L2214" href="#L2214">2214</a><a id="L2215" href="#L2215">2215</a><a id="L2216" href="#L2216">2216</a><a id="L2217" href="#L2217">2217</a><a id="L2218" href="#L2218">2218</a><a id="L2219" href="#L2219">2219</a><a id="L2220" href="#L2220">2220</a><a id="L2221" href="#L2221">2221</a><a id="L2222" href="#L2222">2222</a><a id="L2223" href="#L2223">2223</a><a id="L2224" href="#L2224">2224</a><a id="L2225" href="#L2225">2225</a><a id="L2226" href="#L2226">2226</a><a id="L2227" href="#L2227">2227</a><a id="L2228" href="#L2228">2228</a><a id="L2229" href="#L2229">2229</a><a id="L2230" href="#L2230">2230</a><a id="L2231" href="#L2231">2231</a><a id="L2232" href="#L2232">2232</a><a id="L2233" href="#L2233">2233</a><a id="L2234" href="#L2234">2234</a><a id="L2235" href="#L2235">2235</a><a id="L2236" href="#L2236">2236</a><a id="L2237" href="#L2237">2237</a><a id="L2238" href="#L2238">2238</a><a id="L2239" href="#L2239">2239</a><a id="L2240" href="#L2240">2240</a><a id="L2241" href="#L2241">2241</a><a id="L2242" href="#L2242">2242</a><a id="L2243" href="#L2243">2243</a><a id="L2244" href="#L2244">2244</a><a id="L2245" href="#L2245">2245</a><a id="L2246" href="#L2246">2246</a><a id="L2247" href="#L2247">2247</a><a id="L2248" href="#L2248">2248</a><a id="L2249" href="#L2249">2249</a><a id="L2250" href="#L2250">2250</a><a id="L2251" href="#L2251">2251</a><a id="L2252" href="#L2252">2252</a><a id="L2253" href="#L2253">2253</a><a id="L2254" href="#L2254">2254</a><a id="L2255" href="#L2255">2255</a><a id="L2256" href="#L2256">2256</a><a id="L2257" href="#L2257">2257</a><a id="L2258" href="#L2258">2258</a><a id="L2259" href="#L2259">2259</a><a id="L2260" href="#L2260">2260</a><a id="L2261" href="#L2261">2261</a><a id="L2262" href="#L2262">2262</a><a id="L2263" href="#L2263">2263</a><a id="L2264" href="#L2264">2264</a><a id="L2265" href="#L2265">2265</a><a id="L2266" href="#L2266">2266</a><a id="L2267" href="#L2267">2267</a><a id="L2268" href="#L2268">2268</a><a id="L2269" href="#L2269">2269</a><a id="L2270" href="#L2270">2270</a><a id="L2271" href="#L2271">2271</a><a id="L2272" href="#L2272">2272</a><a id="L2273" href="#L2273">2273</a><a id="L2274" href="#L2274">2274</a><a id="L2275" href="#L2275">2275</a><a id="L2276" href="#L2276">2276</a><a id="L2277" href="#L2277">2277</a><a id="L2278" href="#L2278">2278</a><a id="L2279" href="#L2279">2279</a><a id="L2280" href="#L2280">2280</a><a id="L2281" href="#L2281">2281</a><a id="L2282" href="#L2282">2282</a><a id="L2283" href="#L2283">2283</a><a id="L2284" href="#L2284">2284</a><a id="L2285" href="#L2285">2285</a><a id="L2286" href="#L2286">2286</a><a id="L2287" href="#L2287">2287</a><a id="L2288" href="#L2288">2288</a><a id="L2289" href="#L2289">2289</a><a id="L2290" href="#L2290">2290</a><a id="L2291" href="#L2291">2291</a><a id="L2292" href="#L2292">2292</a><a id="L2293" href="#L2293">2293</a><a id="L2294" href="#L2294">2294</a><a id="L2295" href="#L2295">2295</a><a id="L2296" href="#L2296">2296</a><a id="L2297" href="#L2297">2297</a><a id="L2298" href="#L2298">2298</a><a id="L2299" href="#L2299">2299</a><a id="L2300" href="#L2300">2300</a><a id="L2301" href="#L2301">2301</a><a id="L2302" href="#L2302">2302</a><a id="L2303" href="#L2303">2303</a><a id="L2304" href="#L2304">2304</a><a id="L2305" href="#L2305">2305</a><a id="L2306" href="#L2306">2306</a><a id="L2307" href="#L2307">2307</a><a id="L2308" href="#L2308">2308</a><a id="L2309" href="#L2309">2309</a><a id="L2310" href="#L2310">2310</a><a id="L2311" href="#L2311">2311</a><a id="L2312" href="#L2312">2312</a><a id="L2313" href="#L2313">2313</a><a id="L2314" href="#L2314">2314</a><a id="L2315" href="#L2315">2315</a><a id="L2316" href="#L2316">2316</a><a id="L2317" href="#L2317">2317</a><a id="L2318" href="#L2318">2318</a><a id="L2319" href="#L2319">2319</a><a id="L2320" href="#L2320">2320</a><a id="L2321" href="#L2321">2321</a><a id="L2322" href="#L2322">2322</a><a id="L2323" href="#L2323">2323</a><a id="L2324" href="#L2324">2324</a><a id="L2325" href="#L2325">2325</a><a id="L2326" href="#L2326">2326</a><a id="L2327" href="#L2327">2327</a><a id="L2328" href="#L2328">2328</a><a id="L2329" href="#L2329">2329</a><a id="L2330" href="#L2330">2330</a><a id="L2331" href="#L2331">2331</a><a id="L2332" href="#L2332">2332</a><a id="L2333" href="#L2333">2333</a><a id="L2334" href="#L2334">2334</a><a id="L2335" href="#L2335">2335</a><a id="L2336" href="#L2336">2336</a><a id="L2337" href="#L2337">2337</a><a id="L2338" href="#L2338">2338</a><a id="L2339" href="#L2339">2339</a><a id="L2340" href="#L2340">2340</a><a id="L2341" href="#L2341">2341</a><a id="L2342" href="#L2342">2342</a><a id="L2343" href="#L2343">2343</a><a id="L2344" href="#L2344">2344</a><a id="L2345" href="#L2345">2345</a><a id="L2346" href="#L2346">2346</a><a id="L2347" href="#L2347">2347</a><a id="L2348" href="#L2348">2348</a><a id="L2349" href="#L2349">2349</a><a id="L2350" href="#L2350">2350</a><a id="L2351" href="#L2351">2351</a><a id="L2352" href="#L2352">2352</a><a id="L2353" href="#L2353">2353</a><a id="L2354" href="#L2354">2354</a><a id="L2355" href="#L2355">2355</a><a id="L2356" href="#L2356">2356</a><a id="L2357" href="#L2357">2357</a><a id="L2358" href="#L2358">2358</a><a id="L2359" href="#L2359">2359</a><a id="L2360" href="#L2360">2360</a><a id="L2361" href="#L2361">2361</a><a id="L2362" href="#L2362">2362</a><a id="L2363" href="#L2363">2363</a><a id="L2364" href="#L2364">2364</a><a id="L2365" href="#L2365">2365</a><a id="L2366" href="#L2366">2366</a><a id="L2367" href="#L2367">2367</a><a id="L2368" href="#L2368">2368</a><a id="L2369" href="#L2369">2369</a><a id="L2370" href="#L2370">2370</a><a id="L2371" href="#L2371">2371</a><a id="L2372" href="#L2372">2372</a><a id="L2373" href="#L2373">2373</a><a id="L2374" href="#L2374">2374</a><a id="L2375" href="#L2375">2375</a><a id="L2376" href="#L2376">2376</a><a id="L2377" href="#L2377">2377</a><a id="L2378" href="#L2378">2378</a><a id="L2379" href="#L2379">2379</a><a id="L2380" href="#L2380">2380</a><a id="L2381" href="#L2381">2381</a><a id="L2382" href="#L2382">2382</a><a id="L2383" href="#L2383">2383</a><a id="L2384" href="#L2384">2384</a><a id="L2385" href="#L2385">2385</a><a id="L2386" href="#L2386">2386</a><a id="L2387" href="#L2387">2387</a><a id="L2388" href="#L2388">2388</a><a id="L2389" href="#L2389">2389</a><a id="L2390" href="#L2390">2390</a><a id="L2391" href="#L2391">2391</a><a id="L2392" href="#L2392">2392</a><a id="L2393" href="#L2393">2393</a><a id="L2394" href="#L2394">2394</a><a id="L2395" href="#L2395">2395</a><a id="L2396" href="#L2396">2396</a><a id="L2397" href="#L2397">2397</a><a id="L2398" href="#L2398">2398</a><a id="L2399" href="#L2399">2399</a><a id="L2400" href="#L2400">2400</a><a id="L2401" href="#L2401">2401</a><a id="L2402" href="#L2402">2402</a><a id="L2403" href="#L2403">2403</a><a id="L2404" href="#L2404">2404</a><a id="L2405" href="#L2405">2405</a><a id="L2406" href="#L2406">2406</a><a id="L2407" href="#L2407">2407</a><a id="L2408" href="#L2408">2408</a><a id="L2409" href="#L2409">2409</a><a id="L2410" href="#L2410">2410</a><a id="L2411" href="#L2411">2411</a><a id="L2412" href="#L2412">2412</a><a id="L2413" href="#L2413">2413</a><a id="L2414" href="#L2414">2414</a><a id="L2415" href="#L2415">2415</a><a id="L2416" href="#L2416">2416</a><a id="L2417" href="#L2417">2417</a><a id="L2418" href="#L2418">2418</a><a id="L2419" href="#L2419">2419</a><a id="L2420" href="#L2420">2420</a><a id="L2421" href="#L2421">2421</a><a id="L2422" href="#L2422">2422</a><a id="L2423" href="#L2423">2423</a><a id="L2424" href="#L2424">2424</a><a id="L2425" href="#L2425">2425</a><a id="L2426" href="#L2426">2426</a><a id="L2427" href="#L2427">2427</a><a id="L2428" href="#L2428">2428</a><a id="L2429" href="#L2429">2429</a><a id="L2430" href="#L2430">2430</a><a id="L2431" href="#L2431">2431</a><a id="L2432" href="#L2432">2432</a><a id="L2433" href="#L2433">2433</a><a id="L2434" href="#L2434">2434</a><a id="L2435" href="#L2435">2435</a><a id="L2436" href="#L2436">2436</a><a id="L2437" href="#L2437">2437</a><a id="L2438" href="#L2438">2438</a><a id="L2439" href="#L2439">2439</a><a id="L2440" href="#L2440">2440</a><a id="L2441" href="#L2441">2441</a><a id="L2442" href="#L2442">2442</a><a id="L2443" href="#L2443">2443</a><a id="L2444" href="#L2444">2444</a><a id="L2445" href="#L2445">2445</a><a id="L2446" href="#L2446">2446</a><a id="L2447" href="#L2447">2447</a><a id="L2448" href="#L2448">2448</a><a id="L2449" href="#L2449">2449</a><a id="L2450" href="#L2450">2450</a><a id="L2451" href="#L2451">2451</a><a id="L2452" href="#L2452">2452</a><a id="L2453" href="#L2453">2453</a><a id="L2454" href="#L2454">2454</a><a id="L2455" href="#L2455">2455</a><a id="L2456" href="#L2456">2456</a><a id="L2457" href="#L2457">2457</a><a id="L2458" href="#L2458">2458</a><a id="L2459" href="#L2459">2459</a><a id="L2460" href="#L2460">2460</a><a id="L2461" href="#L2461">2461</a><a id="L2462" href="#L2462">2462</a><a id="L2463" href="#L2463">2463</a><a id="L2464" href="#L2464">2464</a><a id="L2465" href="#L2465">2465</a><a id="L2466" href="#L2466">2466</a><a id="L2467" href="#L2467">2467</a><a id="L2468" href="#L2468">2468</a><a id="L2469" href="#L2469">2469</a><a id="L2470" href="#L2470">2470</a><a id="L2471" href="#L2471">2471</a><a id="L2472" href="#L2472">2472</a><a id="L2473" href="#L2473">2473</a><a id="L2474" href="#L2474">2474</a><a id="L2475" href="#L2475">2475</a><a id="L2476" href="#L2476">2476</a><a id="L2477" href="#L2477">2477</a><a id="L2478" href="#L2478">2478</a><a id="L2479" href="#L2479">2479</a><a id="L2480" href="#L2480">2480</a><a id="L2481" href="#L2481">2481</a><a id="L2482" href="#L2482">2482</a><a id="L2483" href="#L2483">2483</a><a id="L2484" href="#L2484">2484</a><a id="L2485" href="#L2485">2485</a><a id="L2486" href="#L2486">2486</a><a id="L2487" href="#L2487">2487</a><a id="L2488" href="#L2488">2488</a><a id="L2489" href="#L2489">2489</a><a id="L2490" href="#L2490">2490</a><a id="L2491" href="#L2491">2491</a><a id="L2492" href="#L2492">2492</a><a id="L2493" href="#L2493">2493</a><a id="L2494" href="#L2494">2494</a><a id="L2495" href="#L2495">2495</a><a id="L2496" href="#L2496">2496</a><a id="L2497" href="#L2497">2497</a><a id="L2498" href="#L2498">2498</a><a id="L2499" href="#L2499">2499</a><a id="L2500" href="#L2500">2500</a><a id="L2501" href="#L2501">2501</a><a id="L2502" href="#L2502">2502</a><a id="L2503" href="#L2503">2503</a><a id="L2504" href="#L2504">2504</a><a id="L2505" href="#L2505">2505</a><a id="L2506" href="#L2506">2506</a><a id="L2507" href="#L2507">2507</a><a id="L2508" href="#L2508">2508</a><a id="L2509" href="#L2509">2509</a><a id="L2510" href="#L2510">2510</a><a id="L2511" href="#L2511">2511</a><a id="L2512" href="#L2512">2512</a><a id="L2513" href="#L2513">2513</a><a id="L2514" href="#L2514">2514</a><a id="L2515" href="#L2515">2515</a><a id="L2516" href="#L2516">2516</a><a id="L2517" href="#L2517">2517</a><a id="L2518" href="#L2518">2518</a><a id="L2519" href="#L2519">2519</a><a id="L2520" href="#L2520">2520</a><a id="L2521" href="#L2521">2521</a><a id="L2522" href="#L2522">2522</a><a id="L2523" href="#L2523">2523</a><a id="L2524" href="#L2524">2524</a><a id="L2525" href="#L2525">2525</a><a id="L2526" href="#L2526">2526</a><a id="L2527" href="#L2527">2527</a><a id="L2528" href="#L2528">2528</a><a id="L2529" href="#L2529">2529</a><a id="L2530" href="#L2530">2530</a><a id="L2531" href="#L2531">2531</a><a id="L2532" href="#L2532">2532</a><a id="L2533" href="#L2533">2533</a><a id="L2534" href="#L2534">2534</a><a id="L2535" href="#L2535">2535</a><a id="L2536" href="#L2536">2536</a><a id="L2537" href="#L2537">2537</a><a id="L2538" href="#L2538">2538</a><a id="L2539" href="#L2539">2539</a><a id="L2540" 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<td><td><pre class="sourcecode">
<span class="lc">// Written in the D programming language</span>

<span class="bc">/**
 * Macros:
 *      WIKI = Phobos/StdMath
 *
 *      TABLE_SV = &lt;table border=1 cellpadding=4 cellspacing=0&gt;
 *              &lt;caption&gt;Special Values&lt;/caption&gt;
 *              $0&lt;/table&gt;
 *      SVH = $(TR $(TH $1) $(TH $2))
 *      SV  = $(TR $(TD $1) $(TD $2))
 *
 *      NAN = $(RED NAN)
 *      SUP = &lt;span style="vertical-align:super;font-size:smaller"&gt;$0&lt;/span&gt;
 *      GAMMA =  &amp;#915;
 *      INTEGRAL = &amp;#8747;
 *      INTEGRATE = $(BIG &amp;#8747;&lt;sub&gt;$(SMALL $1)&lt;/sub&gt;&lt;sup&gt;$2&lt;/sup&gt;)
 *      POWER = $1&lt;sup&gt;$2&lt;/sup&gt;
 *      SUB = $1&lt;sub&gt;$2&lt;/sub&gt;
 *      BIGSUM = $(BIG &amp;Sigma; &lt;sup&gt;$2&lt;/sup&gt;&lt;sub&gt;$(SMALL $1)&lt;/sub&gt;)
 *      CHOOSE = $(BIG &amp;#40;) &lt;sup&gt;$(SMALL $1)&lt;/sup&gt;&lt;sub&gt;$(SMALL $2)&lt;/sub&gt; $(BIG &amp;#41;)
 *      PLUSMN = &amp;plusmn;
 *      INFIN = &amp;infin;
 *      PLUSMNINF = &amp;plusmn;&amp;infin;
 *      PI = &amp;pi;
 *      LT = &amp;lt;
 *      GT = &amp;gt;
 */</span>

<span class="bc">/*
 * Authors:
 *      Walter Bright, Don Clugston
 * Copyright:
 *      Copyright (c) 2001-2005 by Digital Mars,
 *      All Rights Reserved,
 *      www.digitalmars.com
 * License:
 *  This software is provided 'as-is', without any express or implied
 *  warranty. In no event will the authors be held liable for any damages
 *  arising from the use of this software.
 *
 *  Permission is granted to anyone to use this software for any purpose,
 *  including commercial applications, and to alter it and redistribute it
 *  freely, subject to the following restrictions:
 *
 *  &lt;ul&gt;
 *  &lt;li&gt; The origin of this software must not be misrepresented; you must not
 *       claim that you wrote the original software. If you use this software
 *       in a product, an acknowledgment in the product documentation would be
 *       appreciated but is not required.
 *  &lt;/li&gt;
 *  &lt;li&gt; Altered source versions must be plainly marked as such, and must not
 *       be misrepresented as being the original software.
 *  &lt;/li&gt;
 *  &lt;li&gt; This notice may not be removed or altered from any source
 *       distribution.
 *  &lt;/li&gt;
 *  &lt;/ul&gt;
 */</span>


<span class="d Compound"><span class="d Module"><span class="k">module</span> <span class="i">std</span>.<span class="i">math</span>;</span>

<span class="lc">//debug=math;           // uncomment to turn on debugging printf's</span>

<span class="d Protection"><span class="k">private</span> <span class="d Import"><span class="k">import</span> <span class="i">std</span>.<span class="i">stdio</span>;</span></span>
<span class="d Protection"><span class="k">private</span> <span class="d Import"><span class="k">import</span> <span class="i">std</span>.<span class="i">c</span>.<span class="i">stdio</span>;</span></span>
<span class="d Protection"><span class="k">private</span> <span class="d Import"><span class="k">import</span> <span class="i">std</span>.<span class="i">string</span>;</span></span>
<span class="d Protection"><span class="k">private</span> <span class="d Import"><span class="k">import</span> <span class="i">std</span>.<span class="i">c</span>.<span class="i">math</span>;</span></span>
<span class="d Protection"><span class="k">private</span> <span class="d Import"><span class="k">import</span> <span class="i">std</span>.<span class="i">traits</span>;</span></span>


<span class="d Protection"><span class="k">private</span>:
<span class="bc">/*
 * The following IEEE 'real' formats are currently supported:
 * 64 bit Big-endian  'double' (eg PowerPC)
 * 128 bit Big-endian 'quadruple' (eg SPARC)
 * 64 bit Little-endian 'double' (eg x86-SSE2)
 * 80 bit Little-endian, with implied bit 'real80' (eg x87, Itanium).
 * 128 bit Little-endian 'quadruple' (not implemented on any known processor!)
 *
 * Non-IEEE 128 bit Big-endian 'doubledouble' (eg PowerPC) has partial support
 */</span>
<span class="d Compound"><span class="d Version"><span class="k">version</span>(<span class="i">LittleEndian</span>) <span class="d Compound">{
    <span class="d StaticAssert"><span class="k">static</span> <span class="k">assert</span>(<span class="e OrOr"><span class="e OrOr"><span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span> == <span class="e Int"><span class="n">53</span></span></span> || <span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>==<span class="e Int"><span class="n">64</span></span></span></span>
               || <span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span> == <span class="e Int"><span class="n">113</span></span></span></span>,
      <span class="e String"><span class="sl">"Only 64-bit, 80-bit, and 128-bit reals"</span>
      <span class="sl">" are supported for LittleEndian CPUs"</span></span>);</span>
}</span> <span class="k">else</span> <span class="d Compound">{
    <span class="d StaticAssert"><span class="k">static</span> <span class="k">assert</span>(<span class="e OrOr"><span class="e OrOr"><span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span> == <span class="e Int"><span class="n">53</span></span></span> || <span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>==<span class="e Int"><span class="n">106</span></span></span></span>
               || <span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span> == <span class="e Int"><span class="n">113</span></span></span></span>,
    <span class="e String"><span class="sl">"Only 64-bit and 128-bit reals are supported for BigEndian CPUs."</span>
    <span class="sl">" double-double reals have partial support"</span></span>);</span>
}</span></span>

<span class="lc">// Constants used for extracting the components of the representation.</span>
<span class="lc">// They supplement the built-in floating point properties.</span>
<span class="d Template"><span class="k">template</span> <span class="i">floatTraits</span><span class="o TemplateParameters">(<span class="o TemplateTypeParameter"><span class="i">T</span></span>)</span> <span class="d Compound">{
 <span class="lc">// EXPMASK is a ushort mask to select the exponent portion (without sign)</span>
 <span class="lc">// POW2MANTDIG = pow(2, real.mant_dig) is the value such that</span>
 <span class="lc">//  (smallest_denormal)*POW2MANTDIG == real.min</span>
 <span class="lc">// EXPPOS_SHORT is the index of the exponent when represented as a ushort array.</span>
 <span class="lc">// SIGNPOS_BYTE is the index of the sign when represented as a ubyte array.</span>
 <span class="d StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e Dot"><span class="e Identifier"><span class="i">T</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span> == <span class="e Int"><span class="n">24</span></span></span>) <span class="d Compound">{ <span class="lc">// float</span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="i">EXPMASK</span> = <span class="e Int"><span class="n">0x7F80</span></span>;</span></span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="i">EXPBIAS</span> = <span class="e Int"><span class="n">0x3F00</span></span>;</span></span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">uint</span></span> <span class="i">EXPMASK_INT</span> = <span class="e Int"><span class="n">0x7F80_0000</span></span>;</span></span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">uint</span></span> <span class="i">MANTISSAMASK_INT</span> = <span class="e Int"><span class="n">0x007F_FFFF</span></span>;</span></span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">POW2MANTDIG</span> = <span class="e Real"><span class="n">0x1p+24</span></span>;</span></span>
    <span class="d Version"><span class="k">version</span>(<span class="i">LittleEndian</span>) <span class="d Compound">{
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">EXPPOS_SHORT</span> = <span class="e Int"><span class="n">1</span></span>;</span></span>
    }</span> <span class="k">else</span> <span class="d Compound">{
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">EXPPOS_SHORT</span> = <span class="e Int"><span class="n">0</span></span>;</span></span>
    }</span></span>
 }</span> <span class="k">else</span> <span class="d StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e Dot"><span class="e Identifier"><span class="i">T</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span> == <span class="e Int"><span class="n">53</span></span></span>) <span class="d Compound">{ <span class="lc">// double, or real==double</span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="i">EXPMASK</span> = <span class="e Int"><span class="n">0x7FF0</span></span>;</span></span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="i">EXPBIAS</span> = <span class="e Int"><span class="n">0x3FE0</span></span>;</span></span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">uint</span></span> <span class="i">EXPMASK_INT</span> = <span class="e Int"><span class="n">0x7FF0_0000</span></span>;</span></span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">uint</span></span> <span class="i">MANTISSAMASK_INT</span> = <span class="e Int"><span class="n">0x000F_FFFF</span></span>;</span></span> <span class="lc">// for the MSB only</span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">POW2MANTDIG</span> = <span class="e Real"><span class="n">0x1p+53</span></span>;</span></span>
    <span class="d Version"><span class="k">version</span>(<span class="i">LittleEndian</span>) <span class="d Compound">{
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">EXPPOS_SHORT</span> = <span class="e Int"><span class="n">3</span></span>;</span></span>
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">SIGNPOS_BYTE</span> = <span class="e Int"><span class="n">7</span></span>;</span></span>
    }</span> <span class="k">else</span> <span class="d Compound">{
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">EXPPOS_SHORT</span> = <span class="e Int"><span class="n">0</span></span>;</span></span>
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">SIGNPOS_BYTE</span> = <span class="e Int"><span class="n">0</span></span>;</span></span>
    }</span></span>
 }</span> <span class="k">else</span> <span class="d StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e Dot"><span class="e Identifier"><span class="i">T</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span> == <span class="e Int"><span class="n">64</span></span></span>) <span class="d Compound">{ <span class="lc">// real80</span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="i">EXPMASK</span> = <span class="e Int"><span class="n">0x7FFF</span></span>;</span></span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="i">EXPBIAS</span> = <span class="e Int"><span class="n">0x3FFE</span></span>;</span></span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">POW2MANTDIG</span> = <span class="e Real"><span class="n">0x1p+63</span></span>;</span></span>
    <span class="d Version"><span class="k">version</span>(<span class="i">LittleEndian</span>) <span class="d Compound">{
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">EXPPOS_SHORT</span> = <span class="e Int"><span class="n">4</span></span>;</span></span>
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">SIGNPOS_BYTE</span> = <span class="e Int"><span class="n">9</span></span>;</span></span>
    }</span> <span class="k">else</span> <span class="d Compound">{
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">EXPPOS_SHORT</span> = <span class="e Int"><span class="n">0</span></span>;</span></span>
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">SIGNPOS_BYTE</span> = <span class="e Int"><span class="n">0</span></span>;</span></span>
    }</span></span>
 }</span> <span class="k">else</span> <span class="d StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span> == <span class="e Int"><span class="n">113</span></span></span>)<span class="d Compound">{ <span class="lc">// quadruple</span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="i">EXPMASK</span> = <span class="e Int"><span class="n">0x7FFF</span></span>;</span></span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">POW2MANTDIG</span> = <span class="e Real"><span class="n">0x1p+113</span></span>;</span></span>
    <span class="d Version"><span class="k">version</span>(<span class="i">LittleEndian</span>) <span class="d Compound">{
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">EXPPOS_SHORT</span> = <span class="e Int"><span class="n">7</span></span>;</span></span>
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">SIGNPOS_BYTE</span> = <span class="e Int"><span class="n">15</span></span>;</span></span>
    }</span> <span class="k">else</span> <span class="d Compound">{
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">EXPPOS_SHORT</span> = <span class="e Int"><span class="n">0</span></span>;</span></span>
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">SIGNPOS_BYTE</span> = <span class="e Int"><span class="n">0</span></span>;</span></span>
    }</span></span>
 }</span> <span class="k">else</span> <span class="d StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span> == <span class="e Int"><span class="n">106</span></span></span>) <span class="d Compound">{ <span class="lc">// doubledouble</span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="i">EXPMASK</span> = <span class="e Int"><span class="n">0x7FF0</span></span>;</span></span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">POW2MANTDIG</span> = <span class="e Real"><span class="n">0x1p+53</span></span>;</span></span>  <span class="lc">// doubledouble denormals are strange</span>
    <span class="lc">// and the exponent byte is not unique</span>
    <span class="d Version"><span class="k">version</span>(<span class="i">LittleEndian</span>) <span class="d Compound">{
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">EXPPOS_SHORT</span> = <span class="e Int"><span class="n">7</span></span>;</span></span> <span class="lc">// [3] is also an exp short</span>
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">SIGNPOS_BYTE</span> = <span class="e Int"><span class="n">15</span></span>;</span></span>
    }</span> <span class="k">else</span> <span class="d Compound">{
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">EXPPOS_SHORT</span> = <span class="e Int"><span class="n">0</span></span>;</span></span> <span class="lc">// [4] is also an exp short</span>
      <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">SIGNPOS_BYTE</span> = <span class="e Int"><span class="n">0</span></span>;</span></span>
    }</span></span>
 }</span></span></span></span></span></span>
}</span></span>

<span class="lc">// These apply to all floating-point types</span>
<span class="d Version"><span class="k">version</span>(<span class="i">LittleEndian</span>) <span class="d Compound">{
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">MANTISSA_LSB</span> = <span class="e Int"><span class="n">0</span></span>;</span></span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">MANTISSA_MSB</span> = <span class="e Int"><span class="n">1</span></span>;</span></span>
}</span> <span class="k">else</span> <span class="d Compound">{
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">MANTISSA_LSB</span> = <span class="e Int"><span class="n">1</span></span>;</span></span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="i">MANTISSA_MSB</span> = <span class="e Int"><span class="n">0</span></span>;</span></span>
}</span></span>
<span class="d Protection"><span class="k">public</span>:

<span class="d Compound"><span class="d Class"><span class="k">class</span> <span class="i">NotImplemented</span> : <span class="t BaseClass"><span class="t Identifier"><span class="i">Error</span></span></span>
<span class="d Compound">{
    <span class="d Constructor"><span class="k">this</span><span class="o Parameters">(<span class="o Parameter"><span class="t Identifier"><span class="i">string</span></span> <span class="i">msg</span></span>)</span>
    <span class="s FuncBody"><span class="s Compound">{
        <span class="s Expression"><span class="e Call"><span class="e Super"><span class="k">super</span></span>(<span class="i">msg</span> ~ <span class="sl">" not implemented"</span>)</span>;</span>
    }</span></span></span>
}</span></span>

<span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">E</span> =          <span class="e Real"><span class="n">2.7182818284590452354L</span></span>;</span></span>  <span class="bc">/** e */</span>
 <span class="lc">// 3.32193 fldl2t</span>
<span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">LOG2T</span> =      <span class="e Real"><span class="n">0x1.a934f0979a3715fcp+1</span></span>;</span></span> <span class="bc">/** log&lt;sub&gt;2&lt;/sub&gt;10 */</span>
 <span class="lc">// 1.4427 fldl2e</span>
<span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">LOG2E</span> =      <span class="e Real"><span class="n">0x1.71547652b82fe178p+0</span></span>;</span></span> <span class="bc">/** log&lt;sub&gt;2&lt;/sub&gt;e */</span>
 <span class="lc">// 0.30103 fldlg2</span>
<span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">LOG2</span> =       <span class="e Real"><span class="n">0x1.34413509f79fef32p-2</span></span>;</span></span> <span class="bc">/** log&lt;sub&gt;10&lt;/sub&gt;2 */</span>
<span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">LOG10E</span> =     <span class="e Real"><span class="n">0.43429448190325182765</span></span>;</span></span>  <span class="bc">/** log&lt;sub&gt;10&lt;/sub&gt;e */</span>
<span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">LN2</span> =        <span class="e Real"><span class="n">0x1.62e42fefa39ef358p-1</span></span>;</span></span> <span class="bc">/** ln 2 */</span>  <span class="lc">// 0.693147 fldln2</span>
<span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">LN10</span> =       <span class="e Real"><span class="n">2.30258509299404568402</span></span>;</span></span>  <span class="bc">/** ln 10 */</span>
<span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">PI</span> =         <span class="e Real"><span class="n">0x1.921fb54442d1846ap+1</span></span>;</span></span> <span class="bc">/** $(_PI) */</span> <span class="lc">// 3.14159 fldpi</span>
<span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">PI_2</span> =       <span class="e Real"><span class="n">1.57079632679489661923</span></span>;</span></span>  <span class="bc">/** $(PI) / 2 */</span>
<span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">PI_4</span> =       <span class="e Real"><span class="n">0.78539816339744830962</span></span>;</span></span>  <span class="bc">/** $(PI) / 4 */</span>
<span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">M_1_PI</span> =     <span class="e Real"><span class="n">0.31830988618379067154</span></span>;</span></span>  <span class="bc">/** 1 / $(PI) */</span>
<span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">M_2_PI</span> =     <span class="e Real"><span class="n">0.63661977236758134308</span></span>;</span></span>  <span class="bc">/** 2 / $(PI) */</span>
<span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">M_2_SQRTPI</span> = <span class="e Real"><span class="n">1.12837916709551257390</span></span>;</span></span>  <span class="bc">/** 2 / &amp;radic;$(PI) */</span>
<span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">SQRT2</span> =      <span class="e Real"><span class="n">1.41421356237309504880</span></span>;</span></span>  <span class="bc">/** &amp;radic;2 */</span>
<span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">SQRT1_2</span> =    <span class="e Real"><span class="n">0.70710678118654752440</span></span>;</span></span>  <span class="bc">/** &amp;radic;&amp;frac12; */</span>

<span class="bc">/*
        Octal versions:
        PI/64800        0.00001 45530 36176 77347 02143 15351 61441 26767
        PI/180          0.01073 72152 11224 72344 25603 54276 63351 22056
        PI/8            0.31103 75524 21026 43021 51423 06305 05600 67016
        SQRT(1/PI)      0.44067 27240 41233 33210 65616 51051 77327 77303
        2/PI            0.50574 60333 44710 40522 47741 16537 21752 32335
        PI/4            0.62207 73250 42055 06043 23046 14612 13401 56034
        SQRT(2/PI)      0.63041 05147 52066 24106 41762 63612 00272 56161

        PI              3.11037 55242 10264 30215 14230 63050 56006 70163
        LOG2            0.23210 11520 47674 77674 61076 11263 26013 37111
 */</span>


<span class="bc">/***********************************
 * Calculates the absolute value
 *
 * For complex numbers, abs(z) = sqrt( $(POWER z.re, 2) + $(POWER z.im, 2) )
 * = hypot(z.re, z.im).
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">abs</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Identifier"><span class="i">fabs</span></span>(<span class="i">x</span>)</span>;</span>
}</span></span></span>

<span class="bc">/** ditto */</span>
<span class="d Function"><span class="t Integral"><span class="k">long</span></span> <span class="i">abs</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">long</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Return"><span class="k">return</span> <span class="e Cond"><span class="e Rel"><span class="e Identifier"><span class="i">x</span></span>&gt;=<span class="e Int"><span class="n">0</span></span></span> ? <span class="e Identifier"><span class="i">x</span></span> : <span class="e Sign">-<span class="e Identifier"><span class="i">x</span></span></span></span>;</span>
}</span></span></span>

<span class="bc">/** ditto */</span>
<span class="d Function"><span class="t Integral"><span class="k">int</span></span> <span class="i">abs</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">int</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Return"><span class="k">return</span> <span class="e Cond"><span class="e Rel"><span class="e Identifier"><span class="i">x</span></span>&gt;=<span class="e Int"><span class="n">0</span></span></span> ? <span class="e Identifier"><span class="i">x</span></span> : <span class="e Sign">-<span class="e Identifier"><span class="i">x</span></span></span></span>;</span>
}</span></span></span>

<span class="bc">/** ditto */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">abs</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">creal</span></span> <span class="i">z</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Identifier"><span class="i">hypot</span></span>(<span class="i">z</span>.<span class="i">re</span>, <span class="i">z</span>.<span class="i">im</span>)</span>;</span>
}</span></span></span>

<span class="bc">/** ditto */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">abs</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">ireal</span></span> <span class="i">y</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Identifier"><span class="i">fabs</span></span>(<span class="i">y</span>.<span class="i">im</span>)</span>;</span>
}</span></span></span>


<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isIdentical</span></span>(<span class="i">abs</span>(-<span class="n">0.0L</span>), <span class="n">0.0L</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isnan</span></span>(<span class="i">abs</span>(<span class="k">real</span>.<span class="i">nan</span>))</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">abs</span></span>(-<span class="k">real</span>.<span class="i">infinity</span>)</span> == <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">abs</span></span>(-<span class="n">3.2Li</span>)</span> == <span class="e Real"><span class="n">3.2L</span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">abs</span></span>(<span class="n">71.6Li</span>)</span> == <span class="e Real"><span class="n">71.6L</span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">abs</span></span>(-<span class="n">56</span>)</span> == <span class="e Int"><span class="n">56</span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">abs</span></span>(<span class="n">2321312L</span>)</span>  == <span class="e Int"><span class="n">2321312L</span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">abs</span></span>(-<span class="n">1</span>+<span class="n">1i</span>)</span> == <span class="e Call"><span class="e Identifier"><span class="i">sqrt</span></span>(<span class="n">2.0</span>)</span></span>)</span>;</span>
}</span></span></span>

<span class="bc">/***********************************
 * Complex conjugate
 *
 *  conj(x + iy) = x - iy
 *
 * Note that z * conj(z) = $(POWER z.re, 2) - $(POWER z.im, 2)
 * is always a real number
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">creal</span></span> <span class="i">conj</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">creal</span></span> <span class="i">z</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Return"><span class="k">return</span> <span class="e Minus"><span class="e Dot"><span class="e Identifier"><span class="i">z</span></span>.<span class="e Identifier"><span class="i">re</span></span></span> - <span class="e Mul"><span class="e Dot"><span class="e Identifier"><span class="i">z</span></span>.<span class="e Identifier"><span class="i">im</span></span></span>*<span class="e Real"><span class="n">1i</span></span></span></span>;</span>
}</span></span></span>

<span class="bc">/** ditto */</span>
<span class="d Function"><span class="t Integral"><span class="k">ireal</span></span> <span class="i">conj</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">ireal</span></span> <span class="i">y</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Return"><span class="k">return</span> <span class="e Sign">-<span class="e Identifier"><span class="i">y</span></span></span>;</span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">conj</span></span>(<span class="n">7</span> + <span class="n">3i</span>)</span> == <span class="e Minus"><span class="e Int"><span class="n">7</span></span>-<span class="e Real"><span class="n">3i</span></span></span></span>)</span>;</span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ireal</span></span> <span class="i">z</span> = <span class="e Sign">-<span class="e Real"><span class="n">3.2Li</span></span></span>;</span></span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">conj</span></span>(<span class="i">z</span>)</span> == <span class="e Sign">-<span class="e Identifier"><span class="i">z</span></span></span></span>)</span>;</span>
}</span></span></span>

<span class="bc">/***********************************
 * Returns cosine of x. x is in radians.
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)                 $(TH cos(x)) $(TH invalid?))
 *      $(TR $(TD $(NAN))            $(TD $(NAN)) $(TD yes)     )
 *      $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD yes)     )
 *      )
 * Bugs:
 *      Results are undefined if |x| &gt;= $(POWER 2,64).
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">cos</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span><span class="s FuncBody">;</span></span>       <span class="bc">/* intrinsic */</span>

<span class="bc">/***********************************
 * Returns sine of x. x is in radians.
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)               $(TH sin(x))      $(TH invalid?))
 *      $(TR $(TD $(NAN))          $(TD $(NAN))      $(TD yes))
 *      $(TR $(TD $(PLUSMN)0.0)    $(TD $(PLUSMN)0.0) $(TD no))
 *      $(TR $(TD $(PLUSMNINF))    $(TD $(NAN))      $(TD yes))
 *      )
 * Bugs:
 *      Results are undefined if |x| &gt;= $(POWER 2,64).
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">sin</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span><span class="s FuncBody">;</span></span>       <span class="bc">/* intrinsic */</span>


<span class="bc">/***********************************
 *  sine, complex and imaginary
 *
 *  sin(z) = sin(z.re)*cosh(z.im) + cos(z.re)*sinh(z.im)i
 *
 * If both sin(&amp;theta;) and cos(&amp;theta;) are required,
 * it is most efficient to use expi(&amp;theta).
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">creal</span></span> <span class="i">sin</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">creal</span></span> <span class="i">z</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
  <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">creal</span></span> <span class="i">cs</span> = <span class="e Call"><span class="e Identifier"><span class="i">expi</span></span>(<span class="i">z</span>.<span class="i">re</span>)</span>;</span></span>
  <span class="s Return"><span class="k">return</span> <span class="e Plus"><span class="e Mul"><span class="e Dot"><span class="e Identifier"><span class="i">cs</span></span>.<span class="e Identifier"><span class="i">im</span></span></span> * <span class="e Call"><span class="e Identifier"><span class="i">cosh</span></span>(<span class="i">z</span>.<span class="i">im</span>)</span></span> + <span class="e Mul"><span class="e Mul"><span class="e Dot"><span class="e Identifier"><span class="i">cs</span></span>.<span class="e Identifier"><span class="i">re</span></span></span> * <span class="e Call"><span class="e Identifier"><span class="i">sinh</span></span>(<span class="i">z</span>.<span class="i">im</span>)</span></span> * <span class="e Real"><span class="n">1i</span></span></span></span>;</span>
}</span></span></span>

<span class="bc">/** ditto */</span>
<span class="d Function"><span class="t Integral"><span class="k">ireal</span></span> <span class="i">sin</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">ireal</span></span> <span class="i">y</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
  <span class="s Return"><span class="k">return</span> <span class="e Mul"><span class="e Call"><span class="e Identifier"><span class="i">cosh</span></span>(<span class="i">y</span>.<span class="i">im</span>)</span>*<span class="e Real"><span class="n">1i</span></span></span>;</span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span> <span class="s FuncBody"><span class="s Compound">{
  <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">sin</span></span>(<span class="n">0.0</span>+<span class="n">0.0i</span>)</span> == <span class="e Real"><span class="n">0.0</span></span></span>)</span>;</span>
  <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">sin</span></span>(<span class="n">2.0</span>+<span class="n">0.0i</span>)</span> == <span class="e Call"><span class="e Identifier"><span class="i">sin</span></span>(<span class="n">2.0L</span>)</span></span> )</span>;</span>
}</span></span></span>

<span class="bc">/***********************************
 *  cosine, complex and imaginary
 *
 *  cos(z) = cos(z.re)*cosh(z.im) - sin(z.re)*sinh(z.im)i
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">creal</span></span> <span class="i">cos</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">creal</span></span> <span class="i">z</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
  <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">creal</span></span> <span class="i">cs</span> = <span class="e Call"><span class="e Identifier"><span class="i">expi</span></span>(<span class="i">z</span>.<span class="i">re</span>)</span>;</span></span>
  <span class="s Return"><span class="k">return</span> <span class="e Minus"><span class="e Mul"><span class="e Dot"><span class="e Identifier"><span class="i">cs</span></span>.<span class="e Identifier"><span class="i">re</span></span></span> * <span class="e Call"><span class="e Identifier"><span class="i">cosh</span></span>(<span class="i">z</span>.<span class="i">im</span>)</span></span> - <span class="e Mul"><span class="e Mul"><span class="e Dot"><span class="e Identifier"><span class="i">cs</span></span>.<span class="e Identifier"><span class="i">im</span></span></span> * <span class="e Call"><span class="e Identifier"><span class="i">sinh</span></span>(<span class="i">z</span>.<span class="i">im</span>)</span></span> * <span class="e Real"><span class="n">1i</span></span></span></span>;</span>
}</span></span></span>

<span class="bc">/** ditto */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">cos</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">ireal</span></span> <span class="i">y</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
  <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Identifier"><span class="i">cosh</span></span>(<span class="i">y</span>.<span class="i">im</span>)</span>;</span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span><span class="s FuncBody"><span class="s Compound">{
  <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">cos</span></span>(<span class="n">0.0</span>+<span class="n">0.0i</span>)</span>==<span class="e Real"><span class="n">1.0</span></span></span>)</span>;</span>
  <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">cos</span></span>(<span class="n">1.3L</span>+<span class="n">0.0i</span>)</span>==<span class="e Call"><span class="e Identifier"><span class="i">cos</span></span>(<span class="n">1.3L</span>)</span></span>)</span>;</span>
  <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">cos</span></span>(<span class="n">5.2Li</span>)</span>== <span class="e Call"><span class="e Identifier"><span class="i">cosh</span></span>(<span class="n">5.2L</span>)</span></span>)</span>;</span>
}</span></span></span>

<span class="bc">/****************************************************************************
 * Returns tangent of x. x is in radians.
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)             $(TH tan(x))       $(TH invalid?))
 *      $(TR $(TD $(NAN))        $(TD $(NAN))       $(TD yes))
 *      $(TR $(TD $(PLUSMN)0.0)  $(TD $(PLUSMN)0.0) $(TD no))
 *      $(TR $(TD $(PLUSMNINF))  $(TD $(NAN))       $(TD yes))
 *      )
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">tan</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s AsmBlock"><span class="k">asm</span>
    {
        <span class="s Asm"><span class="i">fld</span>     <span class="e AsmPostBracket"><span class="e Identifier"><span class="i">x</span></span>[<span class="e AsmRegister"><span class="i">EBP</span></span>]</span>                  ;</span> <span class="lc">// load theta</span>
        <span class="s Asm"><span class="i">fxam</span>                            ;</span> <span class="lc">// test for oddball values</span>
        <span class="s Asm"><span class="i">fstsw</span>   <span class="e AsmRegister"><span class="i">AX</span></span>                      ;</span>
        <span class="s Asm"><span class="i">sahf</span>                            ;</span>
        <span class="s Asm"><span class="i">jc</span>      <span class="e Identifier"><span class="i">trigerr</span></span>                 ;</span> <span class="lc">// x is NAN, infinity, or empty</span>
                                          <span class="lc">// 387's can handle denormals</span>
<span class="s Labeled"><span class="i">SC18</span>:   <span class="s Asm"><span class="i">fptan</span>                           ;</span></span>
        <span class="s Asm"><span class="i">fstp</span>    <span class="e AsmRegister"><span class="i">ST</span>(<span class="n">0</span>)</span>                   ;</span> <span class="lc">// dump X, which is always 1</span>
        <span class="s Asm"><span class="i">fstsw</span>   <span class="e AsmRegister"><span class="i">AX</span></span>                      ;</span>
        <span class="s Asm"><span class="i">sahf</span>                            ;</span>
        <span class="s Asm"><span class="i">jnp</span>     <span class="e Identifier"><span class="i">Lret</span></span>                    ;</span> <span class="lc">// C2 = 1 (x is out of range)</span>

        <span class="lc">// Do argument reduction to bring x into range</span>
        <span class="s Asm"><span class="i">fldpi</span>                           ;</span>
        <span class="s Asm"><span class="i">fxch</span>                            ;</span>
<span class="s Labeled"><span class="i">SC17</span>:   <span class="s Asm"><span class="i">fprem1</span>                          ;</span></span>
        <span class="s Asm"><span class="i">fstsw</span>   <span class="e AsmRegister"><span class="i">AX</span></span>                      ;</span>
        <span class="s Asm"><span class="i">sahf</span>                            ;</span>
        <span class="s Asm"><span class="i">jp</span>      <span class="e Identifier"><span class="i">SC17</span></span>                    ;</span>
        <span class="s Asm"><span class="i">fstp</span>    <span class="e AsmRegister"><span class="i">ST</span>(<span class="n">1</span>)</span>                   ;</span> <span class="lc">// remove pi from stack</span>
        <span class="s Asm"><span class="i">jmp</span>     <span class="e Identifier"><span class="i">SC18</span></span>                    ;</span>

<span class="s Labeled"><span class="i">trigerr</span>:
        <span class="s Asm"><span class="i">jnp</span>     <span class="e Identifier"><span class="i">Lret</span></span>                    ;</span></span> <span class="lc">// if theta is NAN, return theta</span>
        <span class="s Asm"><span class="i">fstp</span>    <span class="e AsmRegister"><span class="i">ST</span>(<span class="n">0</span>)</span>                   ;</span> <span class="lc">// dump theta</span>
    }</span>
    <span class="s Return"><span class="k">return</span> <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">nan</span></span>;</span>

<span class="s Labeled"><span class="i">Lret</span>:
    <span class="s Empty">;</span></span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="d StorageClass"><span class="k">static</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">vals</span><span class="t Array">[]<span class="t Array">[<span class="e Int"><span class="n">2</span></span>]</span></span> =     <span class="lc">// angle,tan</span>
    <span class="e ArrayInit">[
            <span class="e ArrayInit">[   <span class="e Int"><span class="n">0</span></span>,   <span class="e Int"><span class="n">0</span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e Real"><span class="n">.5</span></span>,  <span class="e Real"><span class="n">.5463024898</span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e Int"><span class="n">1</span></span>,   <span class="e Real"><span class="n">1.557407725</span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e Real"><span class="n">1.5</span></span>, <span class="e Real"><span class="n">14.10141995</span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e Int"><span class="n">2</span></span>,  <span class="e Sign">-<span class="e Real"><span class="n">2.185039863</span></span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e Real"><span class="n">2.5</span></span>,<span class="e Sign">-<span class="e Real"><span class="n">.7470222972</span></span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e Int"><span class="n">3</span></span>,  <span class="e Sign">-<span class="e Real"><span class="n">.1425465431</span></span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e Real"><span class="n">3.5</span></span>, <span class="e Real"><span class="n">.3745856402</span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e Int"><span class="n">4</span></span>,   <span class="e Real"><span class="n">1.157821282</span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e Real"><span class="n">4.5</span></span>, <span class="e Real"><span class="n">4.637332055</span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e Int"><span class="n">5</span></span>,  <span class="e Sign">-<span class="e Real"><span class="n">3.380515006</span></span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e Real"><span class="n">5.5</span></span>,<span class="e Sign">-<span class="e Real"><span class="n">.9955840522</span></span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e Int"><span class="n">6</span></span>,  <span class="e Sign">-<span class="e Real"><span class="n">.2910061914</span></span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e Real"><span class="n">6.5</span></span>, <span class="e Real"><span class="n">.2202772003</span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e Int"><span class="n">10</span></span>,  <span class="e Real"><span class="n">.6483608275</span></span>]</span>,

            <span class="lc">// special angles</span>
            <span class="e ArrayInit">[   <span class="e Identifier"><span class="i">PI_4</span></span>,   <span class="e Int"><span class="n">1</span></span>]</span>,
            <span class="lc">//[ PI_2,   real.infinity],</span>
            <span class="e ArrayInit">[   <span class="e Mul"><span class="e Int"><span class="n">3</span></span>*<span class="e Identifier"><span class="i">PI_4</span></span></span>, <span class="e Sign">-<span class="e Int"><span class="n">1</span></span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e Identifier"><span class="i">PI</span></span>,     <span class="e Int"><span class="n">0</span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e Mul"><span class="e Int"><span class="n">5</span></span>*<span class="e Identifier"><span class="i">PI_4</span></span></span>, <span class="e Int"><span class="n">1</span></span>]</span>,
            <span class="lc">//[ 3*PI_2, -real.infinity],</span>
            <span class="e ArrayInit">[   <span class="e Mul"><span class="e Int"><span class="n">7</span></span>*<span class="e Identifier"><span class="i">PI_4</span></span></span>, <span class="e Sign">-<span class="e Int"><span class="n">1</span></span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e Mul"><span class="e Int"><span class="n">2</span></span>*<span class="e Identifier"><span class="i">PI</span></span></span>,   <span class="e Int"><span class="n">0</span></span>]</span>,

            <span class="lc">// overflow</span>
            <span class="e ArrayInit">[   <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span>,  <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">nan</span></span>]</span>,
            <span class="e ArrayInit">[   <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">nan</span></span>,       <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">nan</span></span>]</span>,
            <span class="lc">//[   1e+100,       real.nan],</span>
    ]</span>;</span></span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">int</span></span> <span class="i">i</span>;</span></span>

    <span class="s For"><span class="k">for</span> (<span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">i</span></span> = <span class="e Int"><span class="n">0</span></span></span>;</span> <span class="e Rel"><span class="e Identifier"><span class="i">i</span></span> &lt; <span class="e Dot"><span class="e Identifier"><span class="i">vals</span></span>.<span class="e Identifier"><span class="i">length</span></span></span></span>; <span class="e PostIncr"><span class="e Identifier"><span class="i">i</span></span>++</span>)
    <span class="s Compound">{
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span> = <span class="e Index"><span class="e Index"><span class="e Identifier"><span class="i">vals</span></span>[<span class="e Identifier"><span class="i">i</span></span>]</span>[<span class="e Int"><span class="n">0</span></span>]</span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">r</span> = <span class="e Index"><span class="e Index"><span class="e Identifier"><span class="i">vals</span></span>[<span class="e Identifier"><span class="i">i</span></span>]</span>[<span class="e Int"><span class="n">1</span></span>]</span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">t</span> = <span class="e Call"><span class="e Identifier"><span class="i">tan</span></span>(<span class="i">x</span>)</span>;</span></span>

        <span class="lc">//printf("tan(%Lg) = %Lg, should be %Lg\n", x, t, r);</span>
        <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">mfeq</span></span>(<span class="i">r</span>, <span class="i">t</span>, <span class="n">.0000001</span>)</span>)</span>;</span>

        <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">x</span></span> = <span class="e Sign">-<span class="e Identifier"><span class="i">x</span></span></span></span>;</span>
        <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">r</span></span> = <span class="e Sign">-<span class="e Identifier"><span class="i">r</span></span></span></span>;</span>
        <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">t</span></span> = <span class="e Call"><span class="e Identifier"><span class="i">tan</span></span>(<span class="i">x</span>)</span></span>;</span>
        <span class="lc">//printf("tan(%Lg) = %Lg, should be %Lg\n", x, t, r);</span>
        <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">mfeq</span></span>(<span class="i">r</span>, <span class="i">t</span>, <span class="n">.0000001</span>)</span>)</span>;</span>
    }</span></span>
}</span></span></span>

<span class="bc">/***************
 * Calculates the arc cosine of x,
 * returning a value ranging from -$(PI)/2 to $(PI)/2.
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)         $(TH acos(x)) $(TH invalid?))
 *      $(TR $(TD $(GT)1.0)  $(TD $(NAN))  $(TD yes))
 *      $(TR $(TD $(LT)-1.0) $(TD $(NAN))  $(TD yes))
 *      $(TR $(TD $(NAN))    $(TD $(NAN))  $(TD yes))
 *  )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">acos</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>               <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">acosl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/***************
 * Calculates the arc sine of x,
 * returning a value ranging from -$(PI)/2 to $(PI)/2.
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)            $(TH asin(x))      $(TH invalid?))
 *      $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no))
 *      $(TR $(TD $(GT)1.0)     $(TD $(NAN))       $(TD yes))
 *      $(TR $(TD $(LT)-1.0)    $(TD $(NAN))       $(TD yes))
 *  )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">asin</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>               <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">asinl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/***************
 * Calculates the arc tangent of x,
 * returning a value ranging from -$(PI)/2 to $(PI)/2.
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)                 $(TH atan(x))      $(TH invalid?))
 *  $(TR $(TD $(PLUSMN)0.0)      $(TD $(PLUSMN)0.0) $(TD no))
 *      $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN))       $(TD yes))
 *  )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">atan</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>               <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">atanl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/***************
 * Calculates the arc tangent of y / x,
 * returning a value ranging from -$(PI) to $(PI).
 *
 *      $(TABLE_SV
 *      $(TR $(TH y)                 $(TH x)            $(TH atan(y, x)))
 *      $(TR $(TD $(NAN))            $(TD anything)     $(TD $(NAN)) )
 *      $(TR $(TD anything)          $(TD $(NAN))       $(TD $(NAN)) )
 *      $(TR $(TD $(PLUSMN)0.0)      $(TD $(GT)0.0)     $(TD $(PLUSMN)0.0) )
 *      $(TR $(TD $(PLUSMN)0.0)      $(TD +0.0)         $(TD $(PLUSMN)0.0) )
 *      $(TR $(TD $(PLUSMN)0.0)      $(TD $(LT)0.0)     $(TD $(PLUSMN)$(PI)))
 *      $(TR $(TD $(PLUSMN)0.0)      $(TD -0.0)         $(TD $(PLUSMN)$(PI)))
 *      $(TR $(TD $(GT)0.0)          $(TD $(PLUSMN)0.0) $(TD $(PI)/2) )
 *      $(TR $(TD $(LT)0.0)          $(TD $(PLUSMN)0.0) $(TD -$(PI)/2) )
 *      $(TR $(TD $(GT)0.0)          $(TD $(INFIN))     $(TD $(PLUSMN)0.0) )
 *      $(TR $(TD $(PLUSMN)$(INFIN)) $(TD anything)     $(TD $(PLUSMN)$(PI)/2))
 *      $(TR $(TD $(GT)0.0)          $(TD -$(INFIN))    $(TD $(PLUSMN)$(PI)) )
 *      $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(INFIN))     $(TD $(PLUSMN)$(PI)/4))
 *      $(TR $(TD $(PLUSMN)$(INFIN)) $(TD -$(INFIN))    $(TD $(PLUSMN)3$(PI)/4))
 *      )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">atan2</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">y</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>      <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">atan2l</span></span></span>(<span class="i">y</span>,<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/***********************************
 * Calculates the hyperbolic cosine of x.
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)                 $(TH cosh(x))      $(TH invalid?))
 *      $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)0.0) $(TD no) )
 *      )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">cosh</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>               <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">coshl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/***********************************
 * Calculates the hyperbolic sine of x.
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)                 $(TH sinh(x))           $(TH invalid?))
 *      $(TR $(TD $(PLUSMN)0.0)      $(TD $(PLUSMN)0.0)      $(TD no))
 *      $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)$(INFIN)) $(TD no))
 *      )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">sinh</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>               <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">sinhl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/***********************************
 * Calculates the hyperbolic tangent of x.
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)                 $(TH tanh(x))      $(TH invalid?))
 *      $(TR $(TD $(PLUSMN)0.0)      $(TD $(PLUSMN)0.0) $(TD no) )
 *      $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)1.0) $(TD no))
 *      )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">tanh</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>               <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">tanhl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="lc">//real acosh(real x)            { return std.c.math.acoshl(x); }</span>
<span class="lc">//real asinh(real x)            { return std.c.math.asinhl(x); }</span>
<span class="lc">//real atanh(real x)            { return std.c.math.atanhl(x); }</span>

<span class="bc">/***********************************
 * Calculates the inverse hyperbolic cosine of x.
 *
 *  Mathematically, acosh(x) = log(x + sqrt( x*x - 1))
 *
 * $(TABLE_DOMRG
 *  $(DOMAIN 1..$(INFIN))
 *  $(RANGE  1..log(real.max), $(INFIN)) )
 *      $(TABLE_SV
 *    $(SVH  x,     acosh(x) )
 *    $(SV  $(NAN), $(NAN) )
 *    $(SV  &lt;1,     $(NAN) )
 *    $(SV  1,      0       )
 *    $(SV  +$(INFIN),+$(INFIN))
 *  )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">acosh</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">x</span></span> &gt; <span class="e Div"><span class="e Int"><span class="n">1</span></span>/<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">epsilon</span></span></span></span>)
        <span class="s Return"><span class="k">return</span> <span class="e Plus"><span class="e Identifier"><span class="i">LN2</span></span> + <span class="e Call"><span class="e Identifier"><span class="i">log</span></span>(<span class="i">x</span>)</span></span>;</span>
    <span class="k">else</span>
        <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Identifier"><span class="i">log</span></span>(<span class="i">x</span> + <span class="i">sqrt</span>(<span class="i">x</span>*<span class="i">x</span> - <span class="n">1</span>))</span>;</span></span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isnan</span></span>(<span class="i">acosh</span>(<span class="n">0.9</span>))</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isnan</span></span>(<span class="i">acosh</span>(<span class="k">real</span>.<span class="i">nan</span>))</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">acosh</span></span>(<span class="n">1</span>)</span>==<span class="e Real"><span class="n">0.0</span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">acosh</span></span>(<span class="k">real</span>.<span class="i">infinity</span>)</span> == <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span></span>)</span>;</span>
}</span></span></span>

<span class="bc">/***********************************
 * Calculates the inverse hyperbolic sine of x.
 *
 *  Mathematically,
 *  ---------------
 *  asinh(x) =  log( x + sqrt( x*x + 1 )) // if x &gt;= +0
 *  asinh(x) = -log(-x + sqrt( x*x + 1 )) // if x &lt;= -0
 *  -------------
 *
 *    $(TABLE_SV
 *    $(SVH x,                asinh(x)       )
 *    $(SV  $(NAN),           $(NAN)         )
 *    $(SV  $(PLUSMN)0,       $(PLUSMN)0      )
 *    $(SV  $(PLUSMN)$(INFIN),$(PLUSMN)$(INFIN))
 *    )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">asinh</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Call"><span class="e Identifier"><span class="i">fabs</span></span>(<span class="i">x</span>)</span> &gt; <span class="e Div"><span class="e Int"><span class="n">1</span></span> / <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">epsilon</span></span></span></span>) <span class="s Compound">{   <span class="lc">// beyond this point, x*x + 1 == x*x</span>
            <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Identifier"><span class="i">copysign</span></span>(<span class="i">LN2</span> + <span class="i">log</span>(<span class="i">fabs</span>(<span class="i">x</span>)), <span class="i">x</span>)</span>;</span>
    }</span> <span class="k">else</span> <span class="s Compound">{
            <span class="lc">// sqrt(x*x + 1) ==  1 + x * x / ( 1 + sqrt(x*x + 1) )</span>
            <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Identifier"><span class="i">copysign</span></span>(<span class="i">log1p</span>(<span class="i">fabs</span>(<span class="i">x</span>) + <span class="i">x</span>*<span class="i">x</span> / (<span class="n">1</span> + <span class="i">sqrt</span>(<span class="i">x</span>*<span class="i">x</span> + <span class="n">1</span>)) ), <span class="i">x</span>)</span>;</span>
    }</span></span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isIdentical</span></span>(<span class="i">asinh</span>(<span class="n">0.0</span>), <span class="n">0.0</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isIdentical</span></span>(<span class="i">asinh</span>(-<span class="n">0.0</span>), -<span class="n">0.0</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">asinh</span></span>(<span class="k">real</span>.<span class="i">infinity</span>)</span> == <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">asinh</span></span>(-<span class="k">real</span>.<span class="i">infinity</span>)</span> == <span class="e Sign">-<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isnan</span></span>(<span class="i">asinh</span>(<span class="k">real</span>.<span class="i">nan</span>))</span>)</span>;</span>
}</span></span></span>

<span class="bc">/***********************************
 * Calculates the inverse hyperbolic tangent of x,
 * returning a value from ranging from -1 to 1.
 *
 * Mathematically, atanh(x) = log( (1+x)/(1-x) ) / 2
 *
 *
 * $(TABLE_DOMRG
 *  $(DOMAIN -$(INFIN)..$(INFIN))
 *  $(RANGE  -1..1) )
 * $(TABLE_SV
 *    $(SVH  x,     acosh(x) )
 *    $(SV  $(NAN), $(NAN) )
 *    $(SV  $(PLUSMN)0, $(PLUSMN)0)
 *    $(SV  -$(INFIN), -0)
 * )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">atanh</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="lc">// log( (1+x)/(1-x) ) == log ( 1 + (2*x)/(1-x) )</span>
    <span class="s Return"><span class="k">return</span>  <span class="e Mul"><span class="e Real"><span class="n">0.5</span></span> * <span class="e Call"><span class="e Identifier"><span class="i">log1p</span></span>( <span class="n">2</span> * <span class="i">x</span> / (<span class="n">1</span> - <span class="i">x</span>) )</span></span>;</span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isIdentical</span></span>(<span class="i">atanh</span>(<span class="n">0.0</span>), <span class="n">0.0</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isIdentical</span></span>(<span class="i">atanh</span>(-<span class="n">0.0</span>),-<span class="n">0.0</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isnan</span></span>(<span class="i">atanh</span>(<span class="k">real</span>.<span class="i">nan</span>))</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isnan</span></span>(<span class="i">atanh</span>(-<span class="k">real</span>.<span class="i">infinity</span>))</span>)</span>;</span>
}</span></span></span>

<span class="bc">/*****************************************
 * Returns x rounded to a long value using the current rounding mode.
 * If the integer value of x is
 * greater than long.max, the result is
 * indeterminate.
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">long</span></span> <span class="i">rndtol</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span><span class="s FuncBody">;</span></span>    <span class="bc">/* intrinsic */</span>


<span class="bc">/*****************************************
 * Returns x rounded to a long value using the FE_TONEAREST rounding mode.
 * If the integer value of x is
 * greater than long.max, the result is
 * indeterminate.
 */</span>
<span class="d Linkage"><span class="k">extern</span> (<span class="i">C</span>) <span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">rndtonl</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span><span class="s FuncBody">;</span></span></span>

<span class="bc">/***************************************
 * Compute square root of x.
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)         $(TH sqrt(x))   $(TH invalid?))
 *      $(TR $(TD -0.0)      $(TD -0.0)      $(TD no))
 *      $(TR $(TD $(LT)0.0)  $(TD $(NAN))    $(TD yes))
 *      $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no))
 *      )
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">float</span></span> <span class="i">sqrt</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">float</span></span> <span class="i">x</span></span>)</span><span class="s FuncBody">;</span></span>    <span class="bc">/* intrinsic */</span>
<span class="d Function"><span class="t Integral"><span class="k">double</span></span> <span class="i">sqrt</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">double</span></span> <span class="i">x</span></span>)</span><span class="s FuncBody">;</span></span>  <span class="bc">/* intrinsic */</span> <span class="lc">/// ditto</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">sqrt</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span><span class="s FuncBody">;</span></span>      <span class="bc">/* intrinsic */</span> <span class="lc">/// ditto</span>

<span class="d Function"><span class="t Integral"><span class="k">creal</span></span> <span class="i">sqrt</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">creal</span></span> <span class="i">z</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">creal</span></span> <span class="i">c</span>;</span></span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span>,<span class="i">y</span>,<span class="i">w</span>,<span class="i">r</span>;</span></span>

    <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">z</span></span> == <span class="e Int"><span class="n">0</span></span></span>)
    <span class="s Compound">{
        <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">c</span></span> = <span class="e Plus"><span class="e Int"><span class="n">0</span></span> + <span class="e Real"><span class="n">0i</span></span></span></span>;</span>
    }</span>
    <span class="k">else</span>
    <span class="s Compound">{
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">z_re</span> = <span class="e Dot"><span class="e Identifier"><span class="i">z</span></span>.<span class="e Identifier"><span class="i">re</span></span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">z_im</span> = <span class="e Dot"><span class="e Identifier"><span class="i">z</span></span>.<span class="e Identifier"><span class="i">im</span></span></span>;</span></span>

        <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">x</span></span> = <span class="e Call"><span class="e Identifier"><span class="i">fabs</span></span>(<span class="i">z_re</span>)</span></span>;</span>
        <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">y</span></span> = <span class="e Call"><span class="e Identifier"><span class="i">fabs</span></span>(<span class="i">z_im</span>)</span></span>;</span>
        <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">x</span></span> &gt;= <span class="e Identifier"><span class="i">y</span></span></span>)
        <span class="s Compound">{
            <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">r</span></span> = <span class="e Div"><span class="e Identifier"><span class="i">y</span></span> / <span class="e Identifier"><span class="i">x</span></span></span></span>;</span>
            <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">w</span></span> = <span class="e Mul"><span class="e Call"><span class="e Identifier"><span class="i">sqrt</span></span>(<span class="i">x</span>)</span> * <span class="e Call"><span class="e Identifier"><span class="i">sqrt</span></span>(<span class="n">0.5</span> * (<span class="n">1</span> + <span class="i">sqrt</span>(<span class="n">1</span> + <span class="i">r</span> * <span class="i">r</span>)))</span></span></span>;</span>
        }</span>
        <span class="k">else</span>
        <span class="s Compound">{
            <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">r</span></span> = <span class="e Div"><span class="e Identifier"><span class="i">x</span></span> / <span class="e Identifier"><span class="i">y</span></span></span></span>;</span>
            <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">w</span></span> = <span class="e Mul"><span class="e Call"><span class="e Identifier"><span class="i">sqrt</span></span>(<span class="i">y</span>)</span> * <span class="e Call"><span class="e Identifier"><span class="i">sqrt</span></span>(<span class="n">0.5</span> * (<span class="i">r</span> + <span class="i">sqrt</span>(<span class="n">1</span> + <span class="i">r</span> * <span class="i">r</span>)))</span></span></span>;</span>
        }</span></span>

        <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">z_re</span></span> &gt;= <span class="e Int"><span class="n">0</span></span></span>)
        <span class="s Compound">{
            <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">c</span></span> = <span class="e Plus"><span class="e Identifier"><span class="i">w</span></span> + <span class="e Mul"><span class="e Paren">(<span class="e Div"><span class="e Identifier"><span class="i">z_im</span></span> / <span class="e Paren">(<span class="e Plus"><span class="e Identifier"><span class="i">w</span></span> + <span class="e Identifier"><span class="i">w</span></span></span>)</span></span>)</span> * <span class="e Real"><span class="n">1.0i</span></span></span></span></span>;</span>
        }</span>
        <span class="k">else</span>
        <span class="s Compound">{
            <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">z_im</span></span> &lt; <span class="e Int"><span class="n">0</span></span></span>)
                <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">w</span></span> = <span class="e Sign">-<span class="e Identifier"><span class="i">w</span></span></span></span>;</span></span>
            <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">c</span></span> = <span class="e Plus"><span class="e Div"><span class="e Identifier"><span class="i">z_im</span></span> / <span class="e Paren">(<span class="e Plus"><span class="e Identifier"><span class="i">w</span></span> + <span class="e Identifier"><span class="i">w</span></span></span>)</span></span> + <span class="e Mul"><span class="e Identifier"><span class="i">w</span></span> * <span class="e Real"><span class="n">1.0i</span></span></span></span></span>;</span>
        }</span></span>
    }</span></span>
    <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">c</span></span>;</span>
}</span></span></span>

<span class="bc">/**********************
 * Calculates e$(SUP x).
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)         $(TH exp(x)))
 *      $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) )
 *      $(TR $(TD -$(INFIN)) $(TD +0.0) )
 *      )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">exp</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>                <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">expl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/**********************
 * Calculates 2$(SUP x).
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)         $(TH exp2(x)))
 *      $(TR $(TD +$(INFIN)) $(TD +$(INFIN)))
 *      $(TR $(TD -$(INFIN)) $(TD +0.0))
 *      )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">exp2</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>               <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">exp2l</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/******************************************
 * Calculates the value of the natural logarithm base (e)
 * raised to the power of x, minus 1.
 *
 * For very small x, expm1(x) is more accurate
 * than exp(x)-1.
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)            $(TH e$(SUP x)-1))
 *      $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0))
 *      $(TR $(TD +$(INFIN))    $(TD +$(INFIN)))
 *      $(TR $(TD -$(INFIN))    $(TD -1.0))
 *      )
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">expm1</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>              <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">expm1l</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/**
 * Calculate cos(y) + i sin(y).
 *
 * On many CPUs (such as x86), this is a very efficient operation;
 * almost twice as fast as calculating sin(y) and cos(y) separately,
 * and is the preferred method when both are required.
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">creal</span></span> <span class="i">expi</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">y</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Version"><span class="k">version</span>(<span class="i">D_InlineAsm_X86</span>)
    <span class="s Compound">{
        <span class="s AsmBlock"><span class="k">asm</span>
        {
            <span class="s Asm"><span class="i">fld</span> <span class="e Identifier"><span class="i">y</span></span>;</span>
            <span class="s Asm"><span class="i">fsincos</span>;</span>
            <span class="s Asm"><span class="i">fxch</span> <span class="e AsmRegister"><span class="i">ST</span>(<span class="n">1</span>)</span>, <span class="e AsmRegister"><span class="i">ST</span>(<span class="n">0</span>)</span>;</span>
        }</span>
    }</span>
    <span class="k">else</span>
    <span class="s Compound">{
        <span class="s Return"><span class="k">return</span> <span class="e Plus"><span class="e Call"><span class="e Identifier"><span class="i">cos</span></span>(<span class="i">y</span>)</span> + <span class="e Mul"><span class="e Call"><span class="e Identifier"><span class="i">sin</span></span>(<span class="i">y</span>)</span>*<span class="e Real"><span class="n">1i</span></span></span></span>;</span>
    }</span></span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">expi</span></span>(<span class="n">1.3e5L</span>)</span> == <span class="e Plus"><span class="e Call"><span class="e Identifier"><span class="i">cos</span></span>(<span class="n">1.3e5L</span>)</span> + <span class="e Mul"><span class="e Call"><span class="e Identifier"><span class="i">sin</span></span>(<span class="n">1.3e5L</span>)</span> * <span class="e Real"><span class="n">1i</span></span></span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">expi</span></span>(<span class="n">0.0L</span>)</span> == <span class="e Plus"><span class="e Int"><span class="n">1L</span></span> + <span class="e Real"><span class="n">0.0Li</span></span></span></span>)</span>;</span>
}</span></span></span>

<span class="bc">/*********************************************************************
 * Separate floating point value into significand and exponent.
 *
 * Returns:
 *      Calculate and return &lt;i&gt;x&lt;/i&gt; and exp such that
 *      value =&lt;i&gt;x&lt;/i&gt;*2$(SUP exp) and
 *      .5 $(LT)= |&lt;i&gt;x&lt;/i&gt;| $(LT) 1.0&lt;br&gt;
 *      &lt;i&gt;x&lt;/i&gt; has same sign as value.
 *
 *      $(TABLE_SV
 *      $(TR $(TH value)           $(TH returns)         $(TH exp))
 *      $(TR $(TD $(PLUSMN)0.0)    $(TD $(PLUSMN)0.0)    $(TD 0))
 *      $(TR $(TD +$(INFIN))       $(TD +$(INFIN))       $(TD int.max))
 *      $(TR $(TD -$(INFIN))       $(TD -$(INFIN))       $(TD int.min))
 *      $(TR $(TD $(PLUSMN)$(NAN)) $(TD $(PLUSMN)$(NAN)) $(TD int.min))
 *      )
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">frexp</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">value</span></span>, <span class="o Parameter"><span class="k">out</span> <span class="t Integral"><span class="k">int</span></span> <span class="i">exp</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span><span class="t Pointer">*</span> <span class="i">vu</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span><span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">value</span></span></span></span>;</span></span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">long</span></span><span class="t Pointer">*</span> <span class="i">vl</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">long</span></span><span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">value</span></span></span></span>;</span></span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">uint</span></span> <span class="i">ex</span>;</span></span>
    <span class="s Declaration"><span class="d Alias"><span class="k">alias</span> <span class="d Variables"><span class="t TemplateInstance"><span class="i">floatTraits</span>!(<span class="o TemplateArguments"><span class="t Integral"><span class="k">real</span></span></span>)</span> <span class="i">F</span>;</span></span></span>

    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">ex</span></span> = <span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">vu</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> &amp; <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span></span></span>;</span>
  <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span> == <span class="e Int"><span class="n">64</span></span></span>) <span class="s Compound">{ <span class="lc">// real80</span>
    <span class="s If"><span class="k">if</span> (<span class="e Identifier"><span class="i">ex</span></span>) <span class="s Compound">{ <span class="lc">// If exponent is non-zero</span>
        <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">ex</span></span> == <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span></span>) <span class="s Compound">{   <span class="lc">// infinity or NaN</span>
            <span class="s If"><span class="k">if</span> (<span class="e And"><span class="e Deref">*<span class="e Identifier"><span class="i">vl</span></span></span> &amp;  <span class="e Int"><span class="n">0x7FFF_FFFF_FFFF_FFFF</span></span></span>) <span class="s Compound">{  <span class="lc">// NaN</span>
                <span class="s Expression"><span class="e OrAssign"><span class="e Deref">*<span class="e Identifier"><span class="i">vl</span></span></span> |= <span class="e Int"><span class="n">0xC000_0000_0000_0000</span></span></span>;</span>  <span class="lc">// convert NaNS to NaNQ</span>
                <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e TypeDotId"><span class="t Integral"><span class="k">int</span></span>.<span class="i">min</span></span></span>;</span>
            }</span> <span class="k">else</span> <span class="s If"><span class="k">if</span> (<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">vu</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> &amp; <span class="e Int"><span class="n">0x8000</span></span></span>) <span class="s Compound">{   <span class="lc">// negative infinity</span>
                <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e TypeDotId"><span class="t Integral"><span class="k">int</span></span>.<span class="i">min</span></span></span>;</span>
            }</span> <span class="k">else</span> <span class="s Compound">{   <span class="lc">// positive infinity</span>
                <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e TypeDotId"><span class="t Integral"><span class="k">int</span></span>.<span class="i">max</span></span></span>;</span>
            }</span></span></span>
        }</span> <span class="k">else</span> <span class="s Compound">{
            <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e Minus"><span class="e Identifier"><span class="i">ex</span></span> - <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPBIAS</span></span></span></span></span>;</span>
            <span class="s Expression"><span class="e Assign"><span class="e Index"><span class="e Identifier"><span class="i">vu</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> =
                <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span>)<span class="e Paren">(<span class="e Or"><span class="e Paren">(<span class="e And"><span class="e Int"><span class="n">0x8000</span></span> &amp; <span class="e Index"><span class="e Identifier"><span class="i">vu</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span></span>)</span> | <span class="e Int"><span class="n">0x3FFE</span></span></span>)</span></span></span>;</span>
        }</span></span>
    }</span> <span class="k">else</span> <span class="s If"><span class="k">if</span> (<span class="e Not">!<span class="e Deref">*<span class="e Identifier"><span class="i">vl</span></span></span></span>) <span class="s Compound">{
        <span class="lc">// value is +-0.0</span>
        <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e Int"><span class="n">0</span></span></span>;</span>
    }</span> <span class="k">else</span> <span class="s Compound">{
        <span class="lc">// denormal</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">int</span></span> <span class="i">i</span> = <span class="e Sign">-<span class="e Int"><span class="n">0x3FFD</span></span></span>;</span></span>
        <span class="s DoWhile"><span class="k">do</span> <span class="s Compound">{
            <span class="s Expression"><span class="e PostDecr"><span class="e Identifier"><span class="i">i</span></span>--</span>;</span>
            <span class="s Expression"><span class="e LShiftAssign"><span class="e Deref">*<span class="e Identifier"><span class="i">vl</span></span></span> &lt;&lt;= <span class="e Int"><span class="n">1</span></span></span>;</span>
        }</span> <span class="k">while</span> (<span class="e Rel"><span class="e Deref">*<span class="e Identifier"><span class="i">vl</span></span></span> &gt; <span class="e Int"><span class="n">0</span></span></span>)</span><span class="s Empty">;</span>
        <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e Identifier"><span class="i">i</span></span></span>;</span>
        <span class="s Expression"><span class="e Assign"><span class="e Index"><span class="e Identifier"><span class="i">vu</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> =
            <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span>)<span class="e Paren">(<span class="e Or"><span class="e Paren">(<span class="e And"><span class="e Int"><span class="n">0x8000</span></span> &amp; <span class="e Index"><span class="e Identifier"><span class="i">vu</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span></span>)</span> | <span class="e Int"><span class="n">0x3FFE</span></span></span>)</span></span></span>;</span>
    }</span></span></span>
  }</span> <span class="k">else</span> <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span> == <span class="e Int"><span class="n">113</span></span></span>) <span class="s Compound">{ <span class="lc">// quadruple      </span>
        <span class="s If"><span class="k">if</span> (<span class="e Identifier"><span class="i">ex</span></span>) <span class="s Compound">{ <span class="lc">// If exponent is non-zero</span>
            <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">ex</span></span> == <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span></span>) <span class="s Compound">{   <span class="lc">// infinity or NaN</span>
                <span class="s If"><span class="k">if</span> (<span class="e Or"><span class="e Index"><span class="e Identifier"><span class="i">vl</span></span>[<span class="e Identifier"><span class="i">MANTISSA_LSB</span></span>]</span> |
                    <span class="e Paren">( <span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">vl</span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span> &amp; <span class="e Int"><span class="n">0x0000_FFFF_FFFF_FFFF</span></span></span>)</span></span>) <span class="s Compound">{  <span class="lc">// NaN</span>
                    <span class="lc">// convert NaNS to NaNQ</span>
                    <span class="s Expression"><span class="e OrAssign"><span class="e Index"><span class="e Identifier"><span class="i">vl</span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span> |= <span class="e Int"><span class="n">0x0000_8000_0000_0000</span></span></span>;</span>
                    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e TypeDotId"><span class="t Integral"><span class="k">int</span></span>.<span class="i">min</span></span></span>;</span>
                }</span> <span class="k">else</span> <span class="s If"><span class="k">if</span> (<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">vu</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> &amp; <span class="e Int"><span class="n">0x8000</span></span></span>) <span class="s Compound">{   <span class="lc">// negative infinity</span>
                    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e TypeDotId"><span class="t Integral"><span class="k">int</span></span>.<span class="i">min</span></span></span>;</span>
                }</span> <span class="k">else</span> <span class="s Compound">{   <span class="lc">// positive infinity</span>
                    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e TypeDotId"><span class="t Integral"><span class="k">int</span></span>.<span class="i">max</span></span></span>;</span>
                }</span></span></span>
            }</span> <span class="k">else</span> <span class="s Compound">{
                <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e Minus"><span class="e Identifier"><span class="i">ex</span></span> - <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPBIAS</span></span></span></span></span>;</span>
                <span class="s Expression"><span class="e Assign"><span class="e Index"><span class="e Identifier"><span class="i">vu</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> =
                   <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span>)<span class="e Paren">(<span class="e Or"><span class="e Paren">(<span class="e And"><span class="e Int"><span class="n">0x8000</span></span> &amp; <span class="e Index"><span class="e Identifier"><span class="i">vu</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span></span>)</span> | <span class="e Int"><span class="n">0x3FFE</span></span></span>)</span></span></span>;</span>
            }</span></span>
        }</span> <span class="k">else</span> <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Paren">(<span class="e Or"><span class="e Index"><span class="e Identifier"><span class="i">vl</span></span>[<span class="e Identifier"><span class="i">MANTISSA_LSB</span></span>]</span> 
                  |<span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">vl</span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span> &amp; <span class="e Int"><span class="n">0x0000_FFFF_FFFF_FFFF</span></span></span>)</span></span>)</span> == <span class="e Int"><span class="n">0</span></span></span>) <span class="s Compound">{
            <span class="lc">// value is +-0.0</span>
            <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e Int"><span class="n">0</span></span></span>;</span>
    }</span> <span class="k">else</span> <span class="s Compound">{
        <span class="lc">// denormal</span>
        <span class="s Expression"><span class="e MulAssign"><span class="e Identifier"><span class="i">value</span></span> *= <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">POW2MANTDIG</span></span></span></span>;</span>
        <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">ex</span></span> = <span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">vu</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> &amp; <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span></span></span>;</span>
        <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e Minus"><span class="e Minus"><span class="e Identifier"><span class="i">ex</span></span> - <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPBIAS</span></span></span></span> - <span class="e Int"><span class="n">113</span></span></span></span>;</span>
        <span class="s Expression"><span class="e Assign"><span class="e Index"><span class="e Identifier"><span class="i">vu</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> = 
                  <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span>)<span class="e Paren">(<span class="e Or"><span class="e Paren">(<span class="e And"><span class="e Int"><span class="n">0x8000</span></span> &amp; <span class="e Index"><span class="e Identifier"><span class="i">vu</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span></span>)</span> | <span class="e Int"><span class="n">0x3FFE</span></span></span>)</span></span></span>;</span>
    }</span></span></span>
  }</span> <span class="k">else</span> <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>==<span class="e Int"><span class="n">53</span></span></span>) <span class="s Compound">{ <span class="lc">// real is double</span>
    <span class="s If"><span class="k">if</span> (<span class="e Identifier"><span class="i">ex</span></span>) <span class="s Compound">{ <span class="lc">// If exponent is non-zero</span>
        <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">ex</span></span> == <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span></span>) <span class="s Compound">{   <span class="lc">// infinity or NaN</span>
            <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Deref">*<span class="e Identifier"><span class="i">vl</span></span></span> == <span class="e Int"><span class="n">0x7FF0_0000_0000_0000</span></span></span>) <span class="s Compound">{  <span class="lc">// positive infinity</span>
                <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e TypeDotId"><span class="t Integral"><span class="k">int</span></span>.<span class="i">max</span></span></span>;</span>
            }</span> <span class="k">else</span> <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Deref">*<span class="e Identifier"><span class="i">vl</span></span></span> == <span class="e Int"><span class="n">0xFFF0_0000_0000_0000</span></span></span>) <span class="s Compound">{ <span class="lc">// negative infinity</span>
                <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e TypeDotId"><span class="t Integral"><span class="k">int</span></span>.<span class="i">min</span></span></span>;</span>
            }</span> <span class="k">else</span> <span class="s Compound">{ <span class="lc">// NaN</span>
                <span class="s Expression"><span class="e OrAssign"><span class="e Deref">*<span class="e Identifier"><span class="i">vl</span></span></span> |= <span class="e Int"><span class="n">0x0008_0000_0000_0000</span></span></span>;</span>  <span class="lc">// convert NaNS to NaNQ</span>
                <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e TypeDotId"><span class="t Integral"><span class="k">int</span></span>.<span class="i">min</span></span></span>;</span>
            }</span></span></span>
        }</span> <span class="k">else</span> <span class="s Compound">{
            <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e URShift"><span class="e Paren">(<span class="e Minus"><span class="e Identifier"><span class="i">ex</span></span> - <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPBIAS</span></span></span></span>)</span> &gt;&gt;&gt; <span class="e Int"><span class="n">4</span></span></span></span>;</span>
            <span class="s Expression"><span class="e Assign"><span class="e Index"><span class="e Identifier"><span class="i">vu</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span>)<span class="e Paren">(<span class="e Or"><span class="e Paren">(<span class="e And"><span class="e Int"><span class="n">0x8000</span></span> &amp; <span class="e Index"><span class="e Identifier"><span class="i">vu</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span></span>)</span> | <span class="e Int"><span class="n">0x3FE0</span></span></span>)</span></span></span>;</span>
        }</span></span>
    }</span> <span class="k">else</span> <span class="s If"><span class="k">if</span> (<span class="e Not">!<span class="e Paren">(<span class="e And"><span class="e Deref">*<span class="e Identifier"><span class="i">vl</span></span></span> &amp; <span class="e Int"><span class="n">0x7FFF_FFFF_FFFF_FFFF</span></span></span>)</span></span>) <span class="s Compound">{
        <span class="lc">// value is +-0.0</span>
        <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e Int"><span class="n">0</span></span></span>;</span>
    }</span> <span class="k">else</span> <span class="s Compound">{
        <span class="lc">// denormal</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="i">sgn</span>;</span></span>
        <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">sgn</span></span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span>)<span class="e Paren">(<span class="e Or"><span class="e Paren">(<span class="e And"><span class="e Int"><span class="n">0x8000</span></span> &amp; <span class="e Index"><span class="e Identifier"><span class="i">vu</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span></span>)</span>| <span class="e Int"><span class="n">0x3FE0</span></span></span>)</span></span></span>;</span>
        <span class="s Expression"><span class="e AndAssign"><span class="e Deref">*<span class="e Identifier"><span class="i">vl</span></span></span> &amp;= <span class="e Int"><span class="n">0x7FFF_FFFF_FFFF_FFFF</span></span></span>;</span>

        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">int</span></span> <span class="i">i</span> = <span class="e Plus"><span class="e Sign">-<span class="e Int"><span class="n">0x3FD</span></span></span>+<span class="e Int"><span class="n">11</span></span></span>;</span></span>
        <span class="s DoWhile"><span class="k">do</span> <span class="s Compound">{
            <span class="s Expression"><span class="e PostDecr"><span class="e Identifier"><span class="i">i</span></span>--</span>;</span>
            <span class="s Expression"><span class="e LShiftAssign"><span class="e Deref">*<span class="e Identifier"><span class="i">vl</span></span></span> &lt;&lt;= <span class="e Int"><span class="n">1</span></span></span>;</span>
        }</span> <span class="k">while</span> (<span class="e Rel"><span class="e Deref">*<span class="e Identifier"><span class="i">vl</span></span></span> &gt; <span class="e Int"><span class="n">0</span></span></span>)</span><span class="s Empty">;</span>
        <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">exp</span></span> = <span class="e Identifier"><span class="i">i</span></span></span>;</span>
        <span class="s Expression"><span class="e Assign"><span class="e Index"><span class="e Identifier"><span class="i">vu</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> = <span class="e Identifier"><span class="i">sgn</span></span></span>;</span>
    }</span></span></span>
  }</span> <span class="k">else</span> <span class="s Compound">{ <span class="lc">//static if(real.mant_dig==106) // doubledouble</span>
    <span class="s Throw"><span class="k">throw</span> <span class="e New"><span class="k">new</span> <span class="t Identifier"><span class="i">NotImplemented</span></span>(<span class="e String"><span class="sl">"frexp"</span></span>)</span>;</span>
  }</span></span></span></span>
  <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">value</span></span>;</span>
}</span></span></span>


<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="d StorageClass"><span class="k">static</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">vals</span><span class="t Array">[]<span class="t Array">[<span class="e Int"><span class="n">3</span></span>]</span></span> =     <span class="lc">// x,frexp,exp</span>
    <span class="e ArrayInit">[
        <span class="e ArrayInit">[<span class="e Real"><span class="n">0.0</span></span>,   <span class="e Real"><span class="n">0.0</span></span>,    <span class="e Int"><span class="n">0</span></span>]</span>,
        <span class="e ArrayInit">[<span class="e Sign">-<span class="e Real"><span class="n">0.0</span></span></span>,  <span class="e Sign">-<span class="e Real"><span class="n">0.0</span></span></span>,   <span class="e Int"><span class="n">0</span></span>]</span>,
        <span class="e ArrayInit">[<span class="e Real"><span class="n">1.0</span></span>,   <span class="e Real"><span class="n">.5</span></span>,     <span class="e Int"><span class="n">1</span></span>]</span>,
        <span class="e ArrayInit">[<span class="e Sign">-<span class="e Real"><span class="n">1.0</span></span></span>,  <span class="e Sign">-<span class="e Real"><span class="n">.5</span></span></span>,    <span class="e Int"><span class="n">1</span></span>]</span>,
        <span class="e ArrayInit">[<span class="e Real"><span class="n">2.0</span></span>,   <span class="e Real"><span class="n">.5</span></span>,     <span class="e Int"><span class="n">2</span></span>]</span>,
    <span class="e ArrayInit">[<span class="e Div"><span class="e TypeDotId"><span class="t Integral"><span class="k">double</span></span>.<span class="i">min</span></span>/<span class="e Real"><span class="n">2.0</span></span></span>, <span class="e Real"><span class="n">.5</span></span>, <span class="e Sign">-<span class="e Int"><span class="n">1022</span></span></span>]</span>,
        <span class="e ArrayInit">[<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span>,<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span>,<span class="e TypeDotId"><span class="t Integral"><span class="k">int</span></span>.<span class="i">max</span></span>]</span>,
        <span class="e ArrayInit">[<span class="e Sign">-<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span></span>,<span class="e Sign">-<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span></span>,<span class="e TypeDotId"><span class="t Integral"><span class="k">int</span></span>.<span class="i">min</span></span>]</span>,
        <span class="e ArrayInit">[<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">nan</span></span>,<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">nan</span></span>,<span class="e TypeDotId"><span class="t Integral"><span class="k">int</span></span>.<span class="i">min</span></span>]</span>,
        <span class="e ArrayInit">[<span class="e Sign">-<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">nan</span></span></span>,<span class="e Sign">-<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">nan</span></span></span>,<span class="e TypeDotId"><span class="t Integral"><span class="k">int</span></span>.<span class="i">min</span></span>]</span>,
    ]</span>;</span></span>

    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">int</span></span> <span class="i">i</span>;</span></span>

    <span class="s For"><span class="k">for</span> (<span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">i</span></span> = <span class="e Int"><span class="n">0</span></span></span>;</span> <span class="e Rel"><span class="e Identifier"><span class="i">i</span></span> &lt; <span class="e Dot"><span class="e Identifier"><span class="i">vals</span></span>.<span class="e Identifier"><span class="i">length</span></span></span></span>; <span class="e PostIncr"><span class="e Identifier"><span class="i">i</span></span>++</span>) <span class="s Compound">{
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span> = <span class="e Index"><span class="e Index"><span class="e Identifier"><span class="i">vals</span></span>[<span class="e Identifier"><span class="i">i</span></span>]</span>[<span class="e Int"><span class="n">0</span></span>]</span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">e</span> = <span class="e Index"><span class="e Index"><span class="e Identifier"><span class="i">vals</span></span>[<span class="e Identifier"><span class="i">i</span></span>]</span>[<span class="e Int"><span class="n">1</span></span>]</span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">int</span></span> <span class="i">exp</span> = <span class="e Index"><span class="e Index"><span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">int</span></span>)<span class="e Identifier"><span class="i">vals</span></span></span>[<span class="e Identifier"><span class="i">i</span></span>]</span>[<span class="e Int"><span class="n">2</span></span>]</span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">int</span></span> <span class="i">eptr</span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">v</span> = <span class="e Call"><span class="e Identifier"><span class="i">frexp</span></span>(<span class="i">x</span>, <span class="i">eptr</span>)</span>;</span></span>
<span class="lc">//        printf("frexp(%La) = %La, should be %La, eptr = %d, should be %d\n",</span>
<span class="lc">//                x, v, e, eptr, exp);</span>
        <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isIdentical</span></span>(<span class="i">e</span>, <span class="i">v</span>)</span>)</span>;</span>
        <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Identifier"><span class="i">exp</span></span> == <span class="e Identifier"><span class="i">eptr</span></span></span>)</span>;</span>

    }</span></span>
   <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span> == <span class="e Int"><span class="n">64</span></span></span>) <span class="s Compound">{
     <span class="d StorageClass"><span class="k">static</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">extendedvals</span><span class="t Array">[]<span class="t Array">[<span class="e Int"><span class="n">3</span></span>]</span></span> = <span class="e ArrayInit">[ <span class="lc">// x,frexp,exp</span>
        <span class="e ArrayInit">[<span class="e Real"><span class="n">0x1.a5f1c2eb3fe4efp+73</span></span>, <span class="e Real"><span class="n">0x1.A5F1C2EB3FE4EFp-1</span></span>,   <span class="e Int"><span class="n">74</span></span>]</span>,    <span class="lc">// normal</span>
        <span class="e ArrayInit">[<span class="e Real"><span class="n">0x1.fa01712e8f0471ap-1064</span></span>,  <span class="e Real"><span class="n">0x1.fa01712e8f0471ap-1</span></span>,     <span class="e Sign">-<span class="e Int"><span class="n">1063</span></span></span>]</span>,
        <span class="e ArrayInit">[<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">min</span></span>,  <span class="e Real"><span class="n">.5</span></span>,     <span class="e Sign">-<span class="e Int"><span class="n">16381</span></span></span>]</span>,
        <span class="e ArrayInit">[<span class="e Div"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">min</span></span>/<span class="e Real"><span class="n">2.0L</span></span></span>, <span class="e Real"><span class="n">.5</span></span>,     <span class="e Sign">-<span class="e Int"><span class="n">16382</span></span></span>]</span>    <span class="lc">// denormal</span>
     ]</span>;</span></span>

    <span class="s For"><span class="k">for</span> (<span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">i</span></span> = <span class="e Int"><span class="n">0</span></span></span>;</span> <span class="e Rel"><span class="e Identifier"><span class="i">i</span></span> &lt; <span class="e Dot"><span class="e Identifier"><span class="i">extendedvals</span></span>.<span class="e Identifier"><span class="i">length</span></span></span></span>; <span class="e PostIncr"><span class="e Identifier"><span class="i">i</span></span>++</span>) <span class="s Compound">{
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span> = <span class="e Index"><span class="e Index"><span class="e Identifier"><span class="i">extendedvals</span></span>[<span class="e Identifier"><span class="i">i</span></span>]</span>[<span class="e Int"><span class="n">0</span></span>]</span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">e</span> = <span class="e Index"><span class="e Index"><span class="e Identifier"><span class="i">extendedvals</span></span>[<span class="e Identifier"><span class="i">i</span></span>]</span>[<span class="e Int"><span class="n">1</span></span>]</span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">int</span></span> <span class="i">exp</span> = <span class="e Index"><span class="e Index"><span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">int</span></span>)<span class="e Identifier"><span class="i">extendedvals</span></span></span>[<span class="e Identifier"><span class="i">i</span></span>]</span>[<span class="e Int"><span class="n">2</span></span>]</span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">int</span></span> <span class="i">eptr</span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">v</span> = <span class="e Call"><span class="e Identifier"><span class="i">frexp</span></span>(<span class="i">x</span>, <span class="i">eptr</span>)</span>;</span></span>
        <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isIdentical</span></span>(<span class="i">e</span>, <span class="i">v</span>)</span>)</span>;</span>
        <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Identifier"><span class="i">exp</span></span> == <span class="e Identifier"><span class="i">eptr</span></span></span>)</span>;</span>

    }</span></span>
    }</span></span>
}</span></span></span>

<span class="bc">/******************************************
 * Extracts the exponent of x as a signed integral value.
 *
 * If x is not a special value, the result is the same as
 * &lt;tt&gt;cast(int)logb(x)&lt;/tt&gt;.
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)                $(TH ilogb(x))     $(TH Range error?))
 *      $(TR $(TD 0)                 $(TD FP_ILOGB0)   $(TD yes))
 *      $(TR $(TD $(PLUSMN)$(INFIN)) $(TD int.max)     $(TD no))
 *      $(TR $(TD $(NAN))            $(TD FP_ILOGBNAN) $(TD no))
 *      )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">int</span></span> <span class="i">ilogb</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>               <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">ilogbl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="d Alias"><span class="k">alias</span> <span class="d Variables"><span class="t Qualified"><span class="t Qualified"><span class="t Qualified"><span class="t Identifier"><span class="i">std</span></span>.<span class="t Identifier"><span class="i">c</span></span></span>.<span class="t Identifier"><span class="i">math</span></span></span>.<span class="t Identifier"><span class="i">FP_ILOGB0</span></span></span>   <span class="i">FP_ILOGB0</span>;</span></span>
<span class="d Alias"><span class="k">alias</span> <span class="d Variables"><span class="t Qualified"><span class="t Qualified"><span class="t Qualified"><span class="t Identifier"><span class="i">std</span></span>.<span class="t Identifier"><span class="i">c</span></span></span>.<span class="t Identifier"><span class="i">math</span></span></span>.<span class="t Identifier"><span class="i">FP_ILOGBNAN</span></span></span> <span class="i">FP_ILOGBNAN</span>;</span></span>


<span class="bc">/*******************************************
 * Compute n * 2$(SUP exp)
 * References: frexp
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">ldexp</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">n</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">int</span></span> <span class="i">exp</span></span>)</span><span class="s FuncBody">;</span></span>    <span class="bc">/* intrinsic */</span>

<span class="bc">/**************************************
 * Calculate the natural logarithm of x.
 *
 *    $(TABLE_SV
 *    $(TR $(TH x)            $(TH log(x))    $(TH divide by 0?) $(TH invalid?))
 *    $(TR $(TD $(PLUSMN)0.0) $(TD -$(INFIN)) $(TD yes)          $(TD no))
 *    $(TR $(TD $(LT)0.0)     $(TD $(NAN))    $(TD no)           $(TD yes))
 *    $(TR $(TD +$(INFIN))    $(TD +$(INFIN)) $(TD no)           $(TD no))
 *    )
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">log</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>                <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">logl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/**************************************
 * Calculate the base-10 logarithm of x.
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)            $(TH log10(x))  $(TH divide by 0?) $(TH invalid?))
 *      $(TR $(TD $(PLUSMN)0.0) $(TD -$(INFIN)) $(TD yes)          $(TD no))
 *      $(TR $(TD $(LT)0.0)     $(TD $(NAN))    $(TD no)           $(TD yes))
 *      $(TR $(TD +$(INFIN))    $(TD +$(INFIN)) $(TD no)           $(TD no))
 *      )
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">log10</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>              <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">log10l</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/******************************************
 *      Calculates the natural logarithm of 1 + x.
 *
 *      For very small x, log1p(x) will be more accurate than
 *      log(1 + x).
 *
 *  $(TABLE_SV
 *  $(TR $(TH x)            $(TH log1p(x))     $(TH divide by 0?) $(TH invalid?))
 *  $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no)           $(TD no))
 *  $(TR $(TD -1.0)         $(TD -$(INFIN))    $(TD yes)          $(TD no))
 *  $(TR $(TD $(LT)-1.0)    $(TD $(NAN))       $(TD no)           $(TD yes))
 *  $(TR $(TD +$(INFIN))    $(TD -$(INFIN))    $(TD no)           $(TD no))
 *  )
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">log1p</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>              <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">log1pl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/***************************************
 * Calculates the base-2 logarithm of x:
 * log&lt;sub&gt;2&lt;/sub&gt;x
 *
 *  $(TABLE_SV
 *  $(TR $(TH x)            $(TH log2(x))   $(TH divide by 0?) $(TH invalid?))
 *  $(TR $(TD $(PLUSMN)0.0) $(TD -$(INFIN)) $(TD yes)          $(TD no) )
 *  $(TR $(TD $(LT)0.0)     $(TD $(NAN))    $(TD no)           $(TD yes) )
 *  $(TR $(TD +$(INFIN))    $(TD +$(INFIN)) $(TD no)           $(TD no) )
 *  )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">log2</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>               <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">log2l</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/*****************************************
 * Extracts the exponent of x as a signed integral value.
 *
 * If x is subnormal, it is treated as if it were normalized.
 * For a positive, finite x:
 *
 * 1 $(LT)= $(I x) * FLT_RADIX$(SUP -logb(x)) $(LT) FLT_RADIX
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)                 $(TH logb(x))   $(TH divide by 0?) )
 *      $(TR $(TD $(PLUSMN)$(INFIN)) $(TD +$(INFIN)) $(TD no))
 *      $(TR $(TD $(PLUSMN)0.0)      $(TD -$(INFIN)) $(TD yes) )
 *      )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">logb</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>               <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">logbl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/************************************
 * Calculates the remainder from the calculation x/y.
 * Returns:
 * The value of x - i * y, where i is the number of times that y can
 * be completely subtracted from x. The result has the same sign as x.
 *
 * $(TABLE_SV
 *  $(TR $(TH x)              $(TH y)             $(TH modf(x, y))   $(TH invalid?))
 *  $(TR $(TD $(PLUSMN)0.0)   $(TD not 0.0)       $(TD $(PLUSMN)0.0) $(TD no))
 *  $(TR $(TD $(PLUSMNINF))   $(TD anything)      $(TD $(NAN))       $(TD yes))
 *  $(TR $(TD anything)       $(TD $(PLUSMN)0.0)  $(TD $(NAN))       $(TD yes))
 *  $(TR $(TD !=$(PLUSMNINF)) $(TD $(PLUSMNINF))  $(TD x)            $(TD no))
 * )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">modf</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="k">inout</span> <span class="t Integral"><span class="k">real</span></span> <span class="i">y</span></span>)</span> <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">modfl</span></span></span>(<span class="i">x</span>,&amp;<span class="i">y</span>)</span>;</span> }</span></span></span>

<span class="bc">/*************************************
 * Efficiently calculates x * 2$(SUP n).
 *
 * scalbn handles underflow and overflow in
 * the same fashion as the basic arithmetic operators.
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)                 $(TH scalb(x)))
 *      $(TR $(TD $(PLUSMNINF))      $(TD $(PLUSMNINF)) )
 *      $(TR $(TD $(PLUSMN)0.0)      $(TD $(PLUSMN)0.0) )
 *      )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">scalbn</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">int</span></span> <span class="i">n</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Version"><span class="k">version</span>(<span class="i">D_InlineAsm_X86</span>) <span class="s Compound">{
        <span class="lc">// scalbnl is not supported on DMD-Windows, so use asm.</span>
        <span class="s AsmBlock"><span class="k">asm</span> {
            <span class="s Asm"><span class="i">fild</span> <span class="e Identifier"><span class="i">n</span></span>;</span>
            <span class="s Asm"><span class="i">fld</span> <span class="e Identifier"><span class="i">x</span></span>;</span>
            <span class="s Asm"><span class="i">fscale</span>;</span>
            <span class="s Asm"><span class="i">fstp</span> <span class="e AsmRegister"><span class="i">ST</span>(<span class="n">1</span>)</span>, <span class="e AsmRegister"><span class="i">ST</span></span>;</span>
        }</span>
    }</span> <span class="k">else</span> <span class="s Compound">{
        <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">scalbnl</span></span></span>(<span class="i">x</span>, <span class="i">n</span>)</span>;</span>
    }</span></span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span> <span class="s FuncBody"><span class="s Compound">{
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">scalbn</span></span>(-<span class="k">real</span>.<span class="i">infinity</span>, <span class="n">5</span>)</span> == <span class="e Sign">-<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span></span></span>)</span>;</span>
}</span></span></span>

<span class="bc">/***************
 * Calculates the cube root of x.
 *
 *      $(TABLE_SV
 *      $(TR $(TH $(I x))            $(TH cbrt(x))           $(TH invalid?))
 *      $(TR $(TD $(PLUSMN)0.0)      $(TD $(PLUSMN)0.0)      $(TD no) )
 *      $(TR $(TD $(NAN))            $(TD $(NAN))            $(TD yes) )
 *      $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)$(INFIN)) $(TD no) )
 *      )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">cbrt</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>               <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">cbrtl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>


<span class="bc">/*******************************
 * Returns |x|
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)                 $(TH fabs(x)))
 *      $(TR $(TD $(PLUSMN)0.0)      $(TD +0.0) )
 *      $(TR $(TD $(PLUSMN)$(INFIN)) $(TD +$(INFIN)) )
 *      )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">fabs</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span><span class="s FuncBody">;</span></span>      <span class="bc">/* intrinsic */</span>


<span class="bc">/***********************************************************************
 * Calculates the length of the
 * hypotenuse of a right-angled triangle with sides of length x and y.
 * The hypotenuse is the value of the square root of
 * the sums of the squares of x and y:
 *
 *      sqrt($(POW x, 2) + $(POW y, 2))
 *
 * Note that hypot(x, y), hypot(y, x) and
 * hypot(x, -y) are equivalent.
 *
 *  $(TABLE_SV
 *  $(TR $(TH x)            $(TH y)            $(TH hypot(x, y)) $(TH invalid?))
 *  $(TR $(TD x)            $(TD $(PLUSMN)0.0) $(TD |x|)         $(TD no))
 *  $(TR $(TD $(PLUSMNINF)) $(TD y)            $(TD +$(INFIN))   $(TD no))
 *  $(TR $(TD $(PLUSMNINF)) $(TD $(NAN))       $(TD +$(INFIN))   $(TD no))
 *  )
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">hypot</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">y</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="bc">/*
     * This is based on code from:
     * Cephes Math Library Release 2.1:  January, 1989
     * Copyright 1984, 1987, 1989 by Stephen L. Moshier
     * Direct inquiries to 30 Frost Street, Cambridge, MA 02140
     */</span>

    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">int</span></span> <span class="i">PRECL</span> = <span class="e Int"><span class="n">32</span></span>;</span></span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">int</span></span> <span class="i">MAXEXPL</span> = <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">max_exp</span></span>;</span></span> <span class="lc">//16384;</span>
    <span class="d StorageClass"><span class="k">const</span> <span class="d Variables"><span class="t Integral"><span class="k">int</span></span> <span class="i">MINEXPL</span> = <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">min_exp</span></span>;</span></span> <span class="lc">//-16384;</span>

    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">xx</span>, <span class="i">yy</span>, <span class="i">b</span>, <span class="i">re</span>, <span class="i">im</span>;</span></span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">int</span></span> <span class="i">ex</span>, <span class="i">ey</span>, <span class="i">e</span>;</span></span>

    <span class="lc">// Note, hypot(INFINITY, NAN) = INFINITY.</span>
    <span class="s If"><span class="k">if</span> (<span class="e OrOr"><span class="e Call"><span class="e Identifier"><span class="i">isinf</span></span>(<span class="i">x</span>)</span> || <span class="e Call"><span class="e Identifier"><span class="i">isinf</span></span>(<span class="i">y</span>)</span></span>)
        <span class="s Return"><span class="k">return</span> <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span>;</span></span>

    <span class="s If"><span class="k">if</span> (<span class="e Call"><span class="e Identifier"><span class="i">isnan</span></span>(<span class="i">x</span>)</span>)
        <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">x</span></span>;</span></span>
    <span class="s If"><span class="k">if</span> (<span class="e Call"><span class="e Identifier"><span class="i">isnan</span></span>(<span class="i">y</span>)</span>)
        <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">y</span></span>;</span></span>

    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">re</span></span> = <span class="e Call"><span class="e Identifier"><span class="i">fabs</span></span>(<span class="i">x</span>)</span></span>;</span>
    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">im</span></span> = <span class="e Call"><span class="e Identifier"><span class="i">fabs</span></span>(<span class="i">y</span>)</span></span>;</span>

    <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">re</span></span> == <span class="e Real"><span class="n">0.0</span></span></span>)
        <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">im</span></span>;</span></span>
    <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">im</span></span> == <span class="e Real"><span class="n">0.0</span></span></span>)
        <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">re</span></span>;</span></span>

    <span class="lc">// Get the exponents of the numbers</span>
    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">xx</span></span> = <span class="e Call"><span class="e Identifier"><span class="i">frexp</span></span>(<span class="i">re</span>, <span class="i">ex</span>)</span></span>;</span>
    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">yy</span></span> = <span class="e Call"><span class="e Identifier"><span class="i">frexp</span></span>(<span class="i">im</span>, <span class="i">ey</span>)</span></span>;</span>

    <span class="lc">// Check if one number is tiny compared to the other</span>
    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">e</span></span> = <span class="e Minus"><span class="e Identifier"><span class="i">ex</span></span> - <span class="e Identifier"><span class="i">ey</span></span></span></span>;</span>
    <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">e</span></span> &gt; <span class="e Identifier"><span class="i">PRECL</span></span></span>)
        <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">re</span></span>;</span></span>
    <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">e</span></span> &lt; <span class="e Sign">-<span class="e Identifier"><span class="i">PRECL</span></span></span></span>)
        <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">im</span></span>;</span></span>

    <span class="lc">// Find approximate exponent e of the geometric mean.</span>
    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">e</span></span> = <span class="e RShift"><span class="e Paren">(<span class="e Plus"><span class="e Identifier"><span class="i">ex</span></span> + <span class="e Identifier"><span class="i">ey</span></span></span>)</span> &gt;&gt; <span class="e Int"><span class="n">1</span></span></span></span>;</span>

    <span class="lc">// Rescale so mean is about 1</span>
    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">xx</span></span> = <span class="e Call"><span class="e Identifier"><span class="i">ldexp</span></span>(<span class="i">re</span>, -<span class="i">e</span>)</span></span>;</span>
    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">yy</span></span> = <span class="e Call"><span class="e Identifier"><span class="i">ldexp</span></span>(<span class="i">im</span>, -<span class="i">e</span>)</span></span>;</span>

    <span class="lc">// Hypotenuse of the right triangle</span>
    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">b</span></span> = <span class="e Call"><span class="e Identifier"><span class="i">sqrt</span></span>(<span class="i">xx</span> * <span class="i">xx</span>  +  <span class="i">yy</span> * <span class="i">yy</span>)</span></span>;</span>

    <span class="lc">// Compute the exponent of the answer.</span>
    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">yy</span></span> = <span class="e Call"><span class="e Identifier"><span class="i">frexp</span></span>(<span class="i">b</span>, <span class="i">ey</span>)</span></span>;</span>
    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">ey</span></span> = <span class="e Plus"><span class="e Identifier"><span class="i">e</span></span> + <span class="e Identifier"><span class="i">ey</span></span></span></span>;</span>

    <span class="lc">// Check it for overflow and underflow.</span>
    <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">ey</span></span> &gt; <span class="e Plus"><span class="e Identifier"><span class="i">MAXEXPL</span></span> + <span class="e Int"><span class="n">2</span></span></span></span>)
    <span class="s Compound">{
        <span class="lc">//return __matherr(_OVERFLOW, INFINITY, x, y, "hypotl");</span>
        <span class="s Return"><span class="k">return</span> <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span>;</span>
    }</span></span>
    <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">ey</span></span> &lt; <span class="e Minus"><span class="e Identifier"><span class="i">MINEXPL</span></span> - <span class="e Int"><span class="n">2</span></span></span></span>)
        <span class="s Return"><span class="k">return</span> <span class="e Real"><span class="n">0.0</span></span>;</span></span>

    <span class="lc">// Undo the scaling</span>
    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">b</span></span> = <span class="e Call"><span class="e Identifier"><span class="i">ldexp</span></span>(<span class="i">b</span>, <span class="i">e</span>)</span></span>;</span>
    <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">b</span></span>;</span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="d StorageClass"><span class="k">static</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">vals</span><span class="t Array">[]<span class="t Array">[<span class="e Int"><span class="n">3</span></span>]</span></span> =     <span class="lc">// x,y,hypot</span>
    <span class="e ArrayInit">[
        <span class="e ArrayInit">[ <span class="e Int"><span class="n">0</span></span>,      <span class="e Int"><span class="n">0</span></span>,      <span class="e Int"><span class="n">0</span></span>]</span>,
        <span class="e ArrayInit">[ <span class="e Int"><span class="n">0</span></span>,      <span class="e Sign">-<span class="e Int"><span class="n">0</span></span></span>,     <span class="e Int"><span class="n">0</span></span>]</span>,
        <span class="e ArrayInit">[ <span class="e Int"><span class="n">3</span></span>,      <span class="e Int"><span class="n">4</span></span>,      <span class="e Int"><span class="n">5</span></span>]</span>,
        <span class="e ArrayInit">[ <span class="e Sign">-<span class="e Int"><span class="n">300</span></span></span>,   <span class="e Sign">-<span class="e Int"><span class="n">400</span></span></span>,   <span class="e Int"><span class="n">500</span></span>]</span>,
        <span class="e ArrayInit">[ <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">min</span></span>, <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">min</span></span>, <span class="e Real"><span class="n">4.75473e-4932L</span></span>]</span>,
        <span class="e ArrayInit">[ <span class="e Div"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">max</span></span>/<span class="e Int"><span class="n">2</span></span></span>, <span class="e Div"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">max</span></span>/<span class="e Int"><span class="n">2</span></span></span>, <span class="e Real"><span class="n">0x1.6a09e667f3bcc908p+16383L</span></span>]</span>,
        <span class="e ArrayInit">[ <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span>, <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">nan</span></span>, <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span>]</span>,
        <span class="e ArrayInit">[ <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">nan</span></span>, <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">nan</span></span>, <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">nan</span></span>]</span>,
    ]</span>;</span></span>

    <span class="s For"><span class="k">for</span> (<span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">int</span></span> <span class="i">i</span> = <span class="e Int"><span class="n">0</span></span>;</span></span> <span class="e Rel"><span class="e Identifier"><span class="i">i</span></span> &lt; <span class="e Dot"><span class="e Identifier"><span class="i">vals</span></span>.<span class="e Identifier"><span class="i">length</span></span></span></span>; <span class="e PostIncr"><span class="e Identifier"><span class="i">i</span></span>++</span>)
    <span class="s Compound">{
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span> = <span class="e Index"><span class="e Index"><span class="e Identifier"><span class="i">vals</span></span>[<span class="e Identifier"><span class="i">i</span></span>]</span>[<span class="e Int"><span class="n">0</span></span>]</span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">y</span> = <span class="e Index"><span class="e Index"><span class="e Identifier"><span class="i">vals</span></span>[<span class="e Identifier"><span class="i">i</span></span>]</span>[<span class="e Int"><span class="n">1</span></span>]</span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">z</span> = <span class="e Index"><span class="e Index"><span class="e Identifier"><span class="i">vals</span></span>[<span class="e Identifier"><span class="i">i</span></span>]</span>[<span class="e Int"><span class="n">2</span></span>]</span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">h</span> = <span class="e Call"><span class="e Identifier"><span class="i">hypot</span></span>(<span class="i">x</span>, <span class="i">y</span>)</span>;</span></span>

        <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">mfeq</span></span>(<span class="i">z</span>, <span class="i">h</span>, <span class="n">.0000001</span>)</span>)</span>;</span>
    }</span></span>
}</span></span></span>

<span class="bc">/**********************************
 * Returns the error function of x.
 *
 * &lt;img src="erf.gif" alt="error function"&gt;
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">erf</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>                <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">erfl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/**********************************
 * Returns the complementary error function of x, which is 1 - erf(x).
 *
 * &lt;img src="erfc.gif" alt="complementary error function"&gt;
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">erfc</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>               <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">erfcl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/***********************************
 * Natural logarithm of gamma function.
 *
 * Returns the base e (2.718...) logarithm of the absolute
 * value of the gamma function of the argument.
 *
 * For reals, lgamma is equivalent to log(fabs(gamma(x))).
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)                 $(TH lgamma(x)) $(TH invalid?))
 *      $(TR $(TD $(NAN))            $(TD $(NAN))    $(TD yes))
 *      $(TR $(TD integer &lt;= 0)      $(TD +$(INFIN)) $(TD yes))
 *      $(TR $(TD $(PLUSMN)$(INFIN)) $(TD +$(INFIN)) $(TD no))
 *      )
 */</span>
<span class="bc">/* Documentation prepared by Don Clugston */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">lgamma</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">lgammal</span></span></span>(<span class="i">x</span>)</span>;</span>

    <span class="lc">// Use etc.gamma.lgamma for those C systems that are missing it</span>
}</span></span></span>

<span class="bc">/***********************************
 *  The Gamma function, $(GAMMA)(x)
 *
 *  $(GAMMA)(x) is a generalisation of the factorial function
 *  to real and complex numbers.
 *  Like x!, $(GAMMA)(x+1) = x*$(GAMMA)(x).
 *
 *  Mathematically, if z.re &gt; 0 then
 *   $(GAMMA)(z) = $(INTEGRATE 0, &amp;infin;) $(POWER t, z-1)$(POWER e, -t) dt
 *
 *    $(TABLE_SV
 *      $(TR $(TH x)              $(TH $(GAMMA)(x))       $(TH invalid?))
 *      $(TR $(TD $(NAN))         $(TD $(NAN))            $(TD yes))
 *      $(TR $(TD $(PLUSMN)0.0)   $(TD $(PLUSMNINF))      $(TD yes))
 *      $(TR $(TD integer $(GT)0) $(TD (x-1)!)            $(TD no))
 *      $(TR $(TD integer $(LT)0) $(TD $(NAN))            $(TD yes))
 *      $(TR $(TD +$(INFIN))      $(TD +$(INFIN))         $(TD no))
 *      $(TR $(TD -$(INFIN))      $(TD $(NAN))            $(TD yes))
 *    )
 *
 *  References:
 *      $(LINK http://en.wikipedia.org/wiki/Gamma_function),
 *      $(LINK http://www.netlib.org/cephes/ldoubdoc.html#gamma)
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">tgamma</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">tgammal</span></span></span>(<span class="i">x</span>)</span>;</span>

    <span class="lc">// Use etc.gamma.tgamma for those C systems that are missing it</span>
}</span></span></span>

<span class="bc">/**************************************
 * Returns the value of x rounded upward to the next integer
 * (toward positive infinity).
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">ceil</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>               <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">ceill</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/**************************************
 * Returns the value of x rounded downward to the next integer
 * (toward negative infinity).
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">floor</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>              <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">floorl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/******************************************
 * Rounds x to the nearest integer value, using the current rounding
 * mode.
 *
 * Unlike the rint functions, nearbyint does not raise the
 * FE_INEXACT exception.
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">nearbyint</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span> <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">nearbyintl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/**********************************
 * Rounds x to the nearest integer value, using the current rounding
 * mode.
 * If the return value is not equal to x, the FE_INEXACT
 * exception is raised.
 * &lt;b&gt;nearbyint&lt;/b&gt; performs
 * the same operation, but does not set the FE_INEXACT exception.
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">rint</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span><span class="s FuncBody">;</span></span>      <span class="bc">/* intrinsic */</span>

<span class="bc">/***************************************
 * Rounds x to the nearest integer value, using the current rounding
 * mode.
 *
 * This is generally the fastest method to convert a floating-point number
 * to an integer. Note that the results from this function
 * depend on the rounding mode, if the fractional part of x is exactly 0.5.
 * If using the default rounding mode (ties round to even integers)
 * lrint(4.5) == 4, lrint(5.5)==6.
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">long</span></span> <span class="i">lrint</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Version"><span class="k">version</span> (<span class="i">linux</span>)
        <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">llrintl</span></span></span>(<span class="i">x</span>)</span>;</span>
    <span class="k">else</span> <span class="s Version"><span class="k">version</span>(<span class="i">D_InlineAsm_X86</span>)
    <span class="s Compound">{
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">long</span></span> <span class="i">n</span>;</span></span>
        <span class="s AsmBlock"><span class="k">asm</span>
        {
            <span class="s Asm"><span class="i">fld</span> <span class="e Identifier"><span class="i">x</span></span>;</span>
            <span class="s Asm"><span class="i">fistp</span> <span class="e Identifier"><span class="i">n</span></span>;</span>
        }</span>
        <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">n</span></span>;</span>
    }</span>
    <span class="k">else</span>
        <span class="s Throw"><span class="k">throw</span> <span class="e New"><span class="k">new</span> <span class="t Identifier"><span class="i">NotImplemented</span></span>(<span class="e String"><span class="sl">"lrint"</span></span>)</span>;</span></span></span>
}</span></span></span>

<span class="bc">/*******************************************
 * Return the value of x rounded to the nearest integer.
 * If the fractional part of x is exactly 0.5, the return value is rounded to
 * the even integer.
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">round</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span> <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">roundl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/**********************************************
 * Return the value of x rounded to the nearest integer.
 *
 * If the fractional part of x is exactly 0.5, the return value is rounded
 * away from zero.
 *
 * Note: Not supported on windows
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">long</span></span> <span class="i">lround</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Version"><span class="k">version</span> (<span class="i">linux</span>)
        <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">llroundl</span></span></span>(<span class="i">x</span>)</span>;</span>
    <span class="k">else</span>
        <span class="s Throw"><span class="k">throw</span> <span class="e New"><span class="k">new</span> <span class="t Identifier"><span class="i">NotImplemented</span></span>(<span class="e String"><span class="sl">"lround"</span></span>)</span>;</span></span>
}</span></span></span>

<span class="bc">/****************************************************
 * Returns the integer portion of x, dropping the fractional portion.
 *
 * This is also known as "chop" rounding.
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">trunc</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span> <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">truncl</span></span></span>(<span class="i">x</span>)</span>;</span> }</span></span></span>

<span class="bc">/****************************************************
 * Calculate the remainder x REM y, following IEC 60559.
 *
 * REM is the value of x - y * n, where n is the integer nearest the exact
 * value of x / y.
 * If |n - x / y| == 0.5, n is even.
 * If the result is zero, it has the same sign as x.
 * Otherwise, the sign of the result is the sign of x / y.
 * Precision mode has no effect on the remainder functions.
 *
 * remquo returns n in the parameter n.
 *
 * $(TABLE_SV
 *  $(TR $(TH x)               $(TH y)            $(TH remainder(x, y)) $(TH n)   $(TH invalid?))
 *  $(TR $(TD $(PLUSMN)0.0)    $(TD not 0.0)      $(TD $(PLUSMN)0.0)    $(TD 0.0) $(TD no))
 *  $(TR $(TD $(PLUSMNINF))    $(TD anything)     $(TD $(NAN))          $(TD ?)   $(TD yes))
 *  $(TR $(TD anything)        $(TD $(PLUSMN)0.0) $(TD $(NAN))          $(TD ?)   $(TD yes))
 *  $(TR $(TD != $(PLUSMNINF)) $(TD $(PLUSMNINF)) $(TD x)               $(TD ?)   $(TD no))
 * )
 *
 * Note: remquo not supported on windows
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">remainder</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">y</span></span>)</span> <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">remainderl</span></span></span>(<span class="i">x</span>, <span class="i">y</span>)</span>;</span> }</span></span></span>

<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">remquo</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">y</span></span>, <span class="o Parameter"><span class="k">out</span> <span class="t Integral"><span class="k">int</span></span> <span class="i">n</span></span>)</span>  <span class="lc">/// ditto</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Version"><span class="k">version</span> (<span class="i">linux</span>)
        <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">remquol</span></span></span>(<span class="i">x</span>, <span class="i">y</span>, &amp;<span class="i">n</span>)</span>;</span>
    <span class="k">else</span>
        <span class="s Throw"><span class="k">throw</span> <span class="e New"><span class="k">new</span> <span class="t Identifier"><span class="i">NotImplemented</span></span>(<span class="e String"><span class="sl">"remquo"</span></span>)</span>;</span></span>
}</span></span></span>

<span class="bc">/*********************************
 * Returns !=0 if e is a NaN.
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">int</span></span> <span class="i">isnan</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
  <span class="s Declaration"><span class="d Alias"><span class="k">alias</span> <span class="d Variables"><span class="t TemplateInstance"><span class="i">floatTraits</span>!(<span class="o TemplateArguments"><span class="t Integral"><span class="k">real</span></span></span>)</span> <span class="i">F</span>;</span></span></span>
  <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>==<span class="e Int"><span class="n">53</span></span></span>) <span class="s Compound">{ <span class="lc">// double</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span><span class="t Pointer">*</span>  <span class="i">p</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>
        <span class="s Return"><span class="k">return</span> <span class="e AndAnd"><span class="e Paren">(<span class="e And"><span class="e Deref">*<span class="e Identifier"><span class="i">p</span></span></span> &amp; <span class="e Equal"><span class="e Int"><span class="n">0x7FF0_0000_0000_0000</span></span> == <span class="e Int"><span class="n">0x7FF0_0000_0000_0000</span></span></span></span>)</span>
             &amp;&amp; <span class="e And"><span class="e Deref">*<span class="e Identifier"><span class="i">p</span></span></span> &amp; <span class="e Int"><span class="n">0x000F_FFFF_FFFF_FFFF</span></span></span></span>;</span>
  }</span> <span class="k">else</span> <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>==<span class="e Int"><span class="n">64</span></span></span>) <span class="s Compound">{     <span class="lc">// real80</span>
        <span class="lc">// Prevent a ridiculous warning</span>
        <span class="lc">// (why does (ushort | ushort) get promoted to int???)</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="i">e</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span>)<span class="e Paren">(<span class="e And"><span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span> &amp; <span class="e Index"><span class="e Paren">(<span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>)</span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span></span>)</span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span><span class="t Pointer">*</span>  <span class="i">ps</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>
        <span class="s Return"><span class="k">return</span> <span class="e AndAnd"><span class="e Equal"><span class="e Identifier"><span class="i">e</span></span> == <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span></span> &amp;&amp;
            <span class="e And"><span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span> &amp; <span class="e Int"><span class="n">0x7FFF_FFFF_FFFF_FFFF</span></span></span></span>;</span> <span class="lc">// not infinity</span>
  }</span> <span class="k">else</span> <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>==<span class="e Int"><span class="n">113</span></span></span>) <span class="s Compound">{  <span class="lc">// quadruple</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="i">e</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span>)<span class="e Paren">(<span class="e And"><span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span> &amp; <span class="e Index"><span class="e Paren">(<span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>)</span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span></span>)</span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span><span class="t Pointer">*</span>  <span class="i">ps</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>
        <span class="s Return"><span class="k">return</span> <span class="e AndAnd"><span class="e Equal"><span class="e Identifier"><span class="i">e</span></span> == <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span></span> &amp;&amp;
           <span class="e Equal"><span class="e Paren">(<span class="e Or"><span class="e Index"><span class="e Identifier"><span class="i">ps</span></span>[<span class="e Identifier"><span class="i">MANTISSA_LSB</span></span>]</span> | <span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">ps</span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span>&amp; <span class="e Int"><span class="n">0x0000_FFFF_FFFF_FFFF</span></span></span>)</span></span>)</span>!=<span class="e Int"><span class="n">0</span></span></span></span>;</span>
  }</span> <span class="k">else</span> <span class="s Compound">{
      <span class="s Return"><span class="k">return</span> <span class="e Equal"><span class="e Identifier"><span class="i">x</span></span>!=<span class="e Identifier"><span class="i">x</span></span></span>;</span>
  }</span></span></span></span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isnan</span></span>(<span class="k">float</span>.<span class="i">nan</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isnan</span></span>(-<span class="k">double</span>.<span class="i">nan</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isnan</span></span>(<span class="k">real</span>.<span class="i">nan</span>)</span>)</span>;</span>

    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Not">!<span class="e Identifier"><span class="i">isnan</span></span></span>(<span class="n">53.6</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Not">!<span class="e Identifier"><span class="i">isnan</span></span></span>(<span class="k">float</span>.<span class="i">infinity</span>)</span>)</span>;</span>
}</span></span></span>

<span class="bc">/*********************************
 * Returns !=0 if e is finite (not infinite or $(NAN)).
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">int</span></span> <span class="i">isfinite</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">e</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Alias"><span class="k">alias</span> <span class="d Variables"><span class="t TemplateInstance"><span class="i">floatTraits</span>!(<span class="o TemplateArguments"><span class="t Integral"><span class="k">real</span></span></span>)</span> <span class="i">F</span>;</span></span></span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span><span class="t Pointer">*</span> <span class="i">pe</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">e</span></span></span></span>;</span></span>
    <span class="s Return"><span class="k">return</span> <span class="e Equal"><span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">pe</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> &amp; <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span></span>)</span> != <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span></span>;</span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isfinite</span></span>(<span class="n">1.23</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Not">!<span class="e Identifier"><span class="i">isfinite</span></span></span>(<span class="k">double</span>.<span class="i">infinity</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Not">!<span class="e Identifier"><span class="i">isfinite</span></span></span>(<span class="k">float</span>.<span class="i">nan</span>)</span>)</span>;</span>
}</span></span></span>


<span class="bc">/*********************************
 * Returns !=0 if x is normalized (not zero, subnormal, infinite, or $(NAN)).
 */</span>

<span class="bc">/* Need one for each format because subnormal floats might
 * be converted to normal reals.
 */</span>

<span class="d Template"><span class="d Compound"><span class="d Function"><span class="t Integral"><span class="k">int</span></span> <span class="i">isnormal</span><span class="o TemplateParameters">(<span class="o TemplateTypeParameter"><span class="i">X</span></span>)</span><span class="o Parameters">(<span class="o Parameter"><span class="t Identifier"><span class="i">X</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Alias"><span class="k">alias</span> <span class="d Variables"><span class="t TemplateInstance"><span class="i">floatTraits</span>!(<span class="o TemplateArguments"><span class="t Identifier"><span class="i">X</span></span></span>)</span> <span class="i">F</span>;</span></span></span>

    <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span>(<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>==<span class="e Int"><span class="n">106</span></span></span>) <span class="s Compound">{ <span class="lc">// doubledouble</span>
        <span class="lc">// doubledouble is normal if the least significant part is normal.</span>
        <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Identifier"><span class="i">isnormal</span></span>((<span class="k">cast</span>(<span class="k">double</span>*)&amp;<span class="i">x</span>)[<span class="i">MANTISSA_LSB</span>])</span>;</span>
    }</span> <span class="k">else</span> <span class="s Compound">{
        <span class="lc">// ridiculous DMD warning</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="i">e</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span>)<span class="e Paren">(<span class="e And"><span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span> &amp; <span class="e Index"><span class="e Paren">(<span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>)</span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span></span>)</span></span>;</span></span>
        <span class="s Return"><span class="k">return</span> <span class="e Paren">(<span class="e AndAnd"><span class="e Equal"><span class="e Identifier"><span class="i">e</span></span> != <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span></span> &amp;&amp; <span class="e Equal"><span class="e Identifier"><span class="i">e</span></span>!=<span class="e Int"><span class="n">0</span></span></span></span>)</span>;</span>
    }</span></span>
}</span></span></span></span></span>


<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">float</span></span> <span class="i">f</span> = <span class="e Int"><span class="n">3</span></span>;</span></span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">double</span></span> <span class="i">d</span> = <span class="e Int"><span class="n">500</span></span>;</span></span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">e</span> = <span class="e Real"><span class="n">10e+48</span></span>;</span></span>

    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isnormal</span></span>(<span class="i">f</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isnormal</span></span>(<span class="i">d</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isnormal</span></span>(<span class="i">e</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">f</span></span> = <span class="e Assign"><span class="e Identifier"><span class="i">d</span></span> = <span class="e Assign"><span class="e Identifier"><span class="i">e</span></span> = <span class="e Int"><span class="n">0</span></span></span></span></span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Not">!<span class="e Identifier"><span class="i">isnormal</span></span></span>(<span class="i">f</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Not">!<span class="e Identifier"><span class="i">isnormal</span></span></span>(<span class="i">d</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Not">!<span class="e Identifier"><span class="i">isnormal</span></span></span>(<span class="i">e</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Not">!<span class="e Identifier"><span class="i">isnormal</span></span></span>(<span class="k">real</span>.<span class="i">infinity</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isnormal</span></span>(-<span class="k">real</span>.<span class="i">max</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Not">!<span class="e Identifier"><span class="i">isnormal</span></span></span>(<span class="k">real</span>.<span class="i">min</span>/<span class="n">4</span>)</span>)</span>;</span>

}</span></span></span>

<span class="bc">/*********************************
 * Is number subnormal? (Also called "denormal".)
 * Subnormals have a 0 exponent and a 0 most significant mantissa bit.
 */</span>

<span class="bc">/* Need one for each format because subnormal floats might
 * be converted to normal reals.
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">int</span></span> <span class="i">issubnormal</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">float</span></span> <span class="i">f</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">uint</span></span> <span class="t Pointer">*</span><span class="i">p</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">uint</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">f</span></span></span></span>;</span></span>
    <span class="s Return"><span class="k">return</span> <span class="e AndAnd"><span class="e Equal"><span class="e Paren">(<span class="e And"><span class="e Deref">*<span class="e Identifier"><span class="i">p</span></span></span> &amp; <span class="e Int"><span class="n">0x7F80_0000</span></span></span>)</span> == <span class="e Int"><span class="n">0</span></span></span> &amp;&amp; <span class="e And"><span class="e Deref">*<span class="e Identifier"><span class="i">p</span></span></span> &amp; <span class="e Int"><span class="n">0x007F_FFFF</span></span></span></span>;</span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">float</span></span> <span class="i">f</span> = <span class="e Real"><span class="n">3.0</span></span>;</span></span>

    <span class="s For"><span class="k">for</span> (<span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">f</span></span> = <span class="e Real"><span class="n">1.0</span></span></span>;</span> <span class="e Call"><span class="e Not">!<span class="e Identifier"><span class="i">issubnormal</span></span></span>(<span class="i">f</span>)</span>; <span class="e DivAssign"><span class="e Identifier"><span class="i">f</span></span> /= <span class="e Int"><span class="n">2</span></span></span>)
        <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Identifier"><span class="i">f</span></span> != <span class="e Int"><span class="n">0</span></span></span>)</span>;</span></span>
}</span></span></span>

<span class="lc">/// ditto</span>

<span class="d Function"><span class="t Integral"><span class="k">int</span></span> <span class="i">issubnormal</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">double</span></span> <span class="i">d</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">uint</span></span> <span class="t Pointer">*</span><span class="i">p</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">uint</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">d</span></span></span></span>;</span></span>
    <span class="s Return"><span class="k">return</span> <span class="e AndAnd"><span class="e Equal"><span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">p</span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span> &amp; <span class="e Int"><span class="n">0x7FF0_0000</span></span></span>)</span> == <span class="e Int"><span class="n">0</span></span></span>
        &amp;&amp; <span class="e Paren">(<span class="e OrOr"><span class="e Index"><span class="e Identifier"><span class="i">p</span></span>[<span class="e Identifier"><span class="i">MANTISSA_LSB</span></span>]</span> || <span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">p</span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span> &amp; <span class="e Int"><span class="n">0x000F_FFFF</span></span></span></span>)</span></span>;</span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">double</span></span> <span class="i">f</span>;</span></span>

    <span class="s For"><span class="k">for</span> (<span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">f</span></span> = <span class="e Int"><span class="n">1</span></span></span>;</span> <span class="e Call"><span class="e Not">!<span class="e Identifier"><span class="i">issubnormal</span></span></span>(<span class="i">f</span>)</span>; <span class="e DivAssign"><span class="e Identifier"><span class="i">f</span></span> /= <span class="e Int"><span class="n">2</span></span></span>)
        <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Identifier"><span class="i">f</span></span> != <span class="e Int"><span class="n">0</span></span></span>)</span>;</span></span>
}</span></span></span>

<span class="lc">/// ditto</span>

<span class="d Function"><span class="t Integral"><span class="k">int</span></span> <span class="i">issubnormal</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Alias"><span class="k">alias</span> <span class="d Variables"><span class="t TemplateInstance"><span class="i">floatTraits</span>!(<span class="o TemplateArguments"><span class="t Integral"><span class="k">real</span></span></span>)</span> <span class="i">F</span>;</span></span></span>
    <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span> == <span class="e Int"><span class="n">53</span></span></span>) <span class="s Compound">{ <span class="lc">// double</span>
        <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Identifier"><span class="i">issubnormal</span></span>(<span class="k">cast</span>(<span class="k">double</span>)<span class="i">x</span>)</span>;</span>
    }</span> <span class="k">else</span> <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span> == <span class="e Int"><span class="n">113</span></span></span>) <span class="s Compound">{ <span class="lc">// quadruple</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="i">e</span> = <span class="e And"><span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span> &amp; <span class="e Index"><span class="e Paren">(<span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>)</span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">long</span></span><span class="t Pointer">*</span>   <span class="i">ps</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">long</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>
        <span class="s Return"><span class="k">return</span> <span class="e Paren">(<span class="e AndAnd"><span class="e Equal"><span class="e Identifier"><span class="i">e</span></span> == <span class="e Int"><span class="n">0</span></span></span> &amp;&amp;
          <span class="e Paren">(<span class="e Equal"><span class="e Paren">(<span class="e Paren">(<span class="e Or"><span class="e Index"><span class="e Identifier"><span class="i">ps</span></span>[<span class="e Identifier"><span class="i">MANTISSA_LSB</span></span>]</span>|<span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">ps</span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span>&amp; <span class="e Int"><span class="n">0x0000_FFFF_FFFF_FFFF</span></span></span>)</span></span>)</span>)</span> !=<span class="e Int"><span class="n">0</span></span></span>)</span></span>)</span>;</span>
    }</span> <span class="k">else</span> <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>==<span class="e Int"><span class="n">64</span></span></span>) <span class="s Compound">{ <span class="lc">// real80</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span><span class="t Pointer">*</span> <span class="i">pe</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">long</span></span><span class="t Pointer">*</span>   <span class="i">ps</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">long</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>

        <span class="s Return"><span class="k">return</span> <span class="e AndAnd"><span class="e Equal"><span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">pe</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> &amp; <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span></span>)</span> == <span class="e Int"><span class="n">0</span></span></span> &amp;&amp; <span class="e Rel"><span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span> &gt; <span class="e Int"><span class="n">0</span></span></span></span>;</span>
    }</span> <span class="k">else</span> <span class="s Compound">{ <span class="lc">// double double</span>
        <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Identifier"><span class="i">issubnormal</span></span>((<span class="k">cast</span>(<span class="k">double</span>*)&amp;<span class="i">x</span>)[<span class="i">MANTISSA_MSB</span>])</span>;</span>
    }</span></span></span></span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">f</span>;</span></span>

    <span class="s For"><span class="k">for</span> (<span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">f</span></span> = <span class="e Int"><span class="n">1</span></span></span>;</span> <span class="e Call"><span class="e Not">!<span class="e Identifier"><span class="i">issubnormal</span></span></span>(<span class="i">f</span>)</span>; <span class="e DivAssign"><span class="e Identifier"><span class="i">f</span></span> /= <span class="e Int"><span class="n">2</span></span></span>)
        <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Identifier"><span class="i">f</span></span> != <span class="e Int"><span class="n">0</span></span></span>)</span>;</span></span>
}</span></span></span>

<span class="bc">/*********************************
 * Return !=0 if e is $(PLUSMN)$(INFIN).
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">int</span></span> <span class="i">isinf</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Alias"><span class="k">alias</span> <span class="d Variables"><span class="t TemplateInstance"><span class="i">floatTraits</span>!(<span class="o TemplateArguments"><span class="t Integral"><span class="k">real</span></span></span>)</span> <span class="i">F</span>;</span></span></span>
    <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span> == <span class="e Int"><span class="n">53</span></span></span>) <span class="s Compound">{ <span class="lc">// double</span>
        <span class="s Return"><span class="k">return</span> <span class="e Equal"><span class="e Paren">(<span class="e And"><span class="e Paren">(<span class="e Deref">*<span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span></span>)</span> &amp; <span class="e Int"><span class="n">0x7FFF_FFFF_FFFF_FFFF</span></span></span>)</span>
                == <span class="e Int"><span class="n">0x7FF8_0000_0000_0000</span></span></span>;</span>
    }</span> <span class="k">else</span> <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span>(<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span> == <span class="e Int"><span class="n">106</span></span></span>) <span class="s Compound">{ <span class="lc">//doubledouble</span>
        <span class="s Return"><span class="k">return</span> <span class="e Equal"><span class="e Paren">(<span class="e And"><span class="e Paren">(<span class="e Index"><span class="e Paren">(<span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>)</span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span>)</span> &amp; <span class="e Int"><span class="n">0x7FFF_FFFF_FFFF_FFFF</span></span></span>)</span>
                    == <span class="e Int"><span class="n">0x7FF8_0000_0000_0000</span></span></span>;</span>
    }</span> <span class="k">else</span> <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span> == <span class="e Int"><span class="n">113</span></span></span>) <span class="s Compound">{ <span class="lc">// quadruple</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">long</span></span><span class="t Pointer">*</span>   <span class="i">ps</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">long</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>
        <span class="s Return"><span class="k">return</span> <span class="e AndAnd"><span class="e Paren">(<span class="e Equal"><span class="e Index"><span class="e Identifier"><span class="i">ps</span></span>[<span class="e Identifier"><span class="i">MANTISSA_LSB</span></span>]</span> == <span class="e Int"><span class="n">0</span></span></span>)</span>
         &amp;&amp; <span class="e Equal"><span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">ps</span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span> &amp; <span class="e Int"><span class="n">0x7FFF_FFFF_FFFF_FFFF</span></span></span>)</span> == <span class="e Int"><span class="n">0x7FFF_0000_0000_0000</span></span></span></span>;</span>
    }</span> <span class="k">else</span> <span class="s Compound">{ <span class="lc">// real80</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="i">e</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span>)<span class="e Paren">(<span class="e And"><span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span> &amp; <span class="e Index"><span class="e Paren">(<span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>)</span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span></span>)</span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span><span class="t Pointer">*</span>  <span class="i">ps</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>

        <span class="s Return"><span class="k">return</span> <span class="e AndAnd"><span class="e Equal"><span class="e Identifier"><span class="i">e</span></span> == <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span></span> &amp;&amp; <span class="e Equal"><span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span> == <span class="e Int"><span class="n">0x8000_0000_0000_0000</span></span></span></span>;</span>
   }</span></span></span></span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isinf</span></span>(<span class="k">float</span>.<span class="i">infinity</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Not">!<span class="e Identifier"><span class="i">isinf</span></span></span>(<span class="k">float</span>.<span class="i">nan</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isinf</span></span>(<span class="k">double</span>.<span class="i">infinity</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isinf</span></span>(-<span class="k">real</span>.<span class="i">infinity</span>)</span>)</span>;</span>

    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">isinf</span></span>(-<span class="n">1.0</span> / <span class="n">0.0</span>)</span>)</span>;</span>
}</span></span></span>

<span class="bc">/*********************************
 * Is the binary representation of x identical to y?
 *
 * Same as ==, except that positive and negative zero are not identical,
 * and two $(NAN)s are identical if they have the same 'payload'.
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">bool</span></span> <span class="i">isIdentical</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">y</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="lc">// We're doing a bitwise comparison so the endianness is irrelevant.</span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">long</span></span><span class="t Pointer">*</span>   <span class="i">pxs</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">long</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">long</span></span><span class="t Pointer">*</span>   <span class="i">pys</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">long</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">y</span></span></span></span>;</span></span>
 <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span> == <span class="e Int"><span class="n">53</span></span></span>)<span class="s Compound">{ <span class="lc">//double</span>
    <span class="s Return"><span class="k">return</span> <span class="e Equal"><span class="e Index"><span class="e Identifier"><span class="i">pxs</span></span>[<span class="e Int"><span class="n">0</span></span>]</span> == <span class="e Index"><span class="e Identifier"><span class="i">pys</span></span>[<span class="e Int"><span class="n">0</span></span>]</span></span>;</span>
 }</span> <span class="k">else</span> <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e OrOr"><span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span> == <span class="e Int"><span class="n">113</span></span></span> || <span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>==<span class="e Int"><span class="n">106</span></span></span></span>) <span class="s Compound">{
      <span class="lc">// quadruple or doubledouble</span>
    <span class="s Return"><span class="k">return</span> <span class="e AndAnd"><span class="e Equal"><span class="e Index"><span class="e Identifier"><span class="i">pxs</span></span>[<span class="e Int"><span class="n">0</span></span>]</span> == <span class="e Index"><span class="e Identifier"><span class="i">pys</span></span>[<span class="e Int"><span class="n">0</span></span>]</span></span> &amp;&amp; <span class="e Equal"><span class="e Index"><span class="e Identifier"><span class="i">pxs</span></span>[<span class="e Int"><span class="n">1</span></span>]</span> == <span class="e Index"><span class="e Identifier"><span class="i">pys</span></span>[<span class="e Int"><span class="n">1</span></span>]</span></span></span>;</span>
 }</span> <span class="k">else</span> <span class="s Compound">{ <span class="lc">// real80</span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span><span class="t Pointer">*</span> <span class="i">pxe</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span><span class="t Pointer">*</span> <span class="i">pye</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">y</span></span></span></span>;</span></span>
    <span class="s Return"><span class="k">return</span> <span class="e AndAnd"><span class="e Equal"><span class="e Index"><span class="e Identifier"><span class="i">pxe</span></span>[<span class="e Int"><span class="n">4</span></span>]</span> == <span class="e Index"><span class="e Identifier"><span class="i">pye</span></span>[<span class="e Int"><span class="n">4</span></span>]</span></span> &amp;&amp; <span class="e Equal"><span class="e Index"><span class="e Identifier"><span class="i">pxs</span></span>[<span class="e Int"><span class="n">0</span></span>]</span> == <span class="e Index"><span class="e Identifier"><span class="i">pys</span></span>[<span class="e Int"><span class="n">0</span></span>]</span></span></span>;</span>
 }</span></span></span>
}</span></span></span>

<span class="bc">/*********************************
 * Return 1 if sign bit of e is set, 0 if not.
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">int</span></span> <span class="i">signbit</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Return"><span class="k">return</span> <span class="e Equal"><span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Paren">(<span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ubyte</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>)</span>[<span class="e Dot"><span class="e TemplateInstance"><span class="i">floatTraits</span>!(<span class="o TemplateArguments"><span class="t Integral"><span class="k">real</span></span></span>)</span>.<span class="e Identifier"><span class="i">SIGNPOS_BYTE</span></span></span>]</span> &amp; <span class="e Int"><span class="n">0x80</span></span></span>)</span> != <span class="e Int"><span class="n">0</span></span></span>;</span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Debug"><span class="k">debug</span> (<span class="i">math</span>) <span class="s Expression"><span class="e Call"><span class="e Identifier"><span class="i">printf</span></span>(<span class="sl">"math.signbit.unittest\n"</span>)</span>;</span></span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Not">!<span class="e Identifier"><span class="i">signbit</span></span></span>(<span class="k">float</span>.<span class="i">nan</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">signbit</span></span>(-<span class="k">float</span>.<span class="i">nan</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Not">!<span class="e Identifier"><span class="i">signbit</span></span></span>(<span class="n">168.1234</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">signbit</span></span>(-<span class="n">168.1234</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Not">!<span class="e Identifier"><span class="i">signbit</span></span></span>(<span class="n">0.0</span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Call"><span class="e Identifier"><span class="i">signbit</span></span>(-<span class="n">0.0</span>)</span>)</span>;</span>
}</span></span></span>

<span class="bc">/*********************************
 * Return a value composed of to with from's sign bit.
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">copysign</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">to</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">from</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ubyte</span></span><span class="t Pointer">*</span> <span class="i">pto</span>   = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ubyte</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">to</span></span></span></span>;</span></span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ubyte</span></span><span class="t Pointer">*</span> <span class="i">pfrom</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ubyte</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">from</span></span></span></span>;</span></span>

    <span class="s Declaration"><span class="d Alias"><span class="k">alias</span> <span class="d Variables"><span class="t TemplateInstance"><span class="i">floatTraits</span>!(<span class="o TemplateArguments"><span class="t Integral"><span class="k">real</span></span></span>)</span> <span class="i">F</span>;</span></span></span>
    <span class="s Expression"><span class="e AndAssign"><span class="e Index"><span class="e Identifier"><span class="i">pto</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">SIGNPOS_BYTE</span></span></span>]</span> &amp;= <span class="e Int"><span class="n">0x7F</span></span></span>;</span>
    <span class="s Expression"><span class="e OrAssign"><span class="e Index"><span class="e Identifier"><span class="i">pto</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">SIGNPOS_BYTE</span></span></span>]</span> |= <span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">pfrom</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">SIGNPOS_BYTE</span></span></span>]</span> &amp; <span class="e Int"><span class="n">0x80</span></span></span></span>;</span>
    <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">to</span></span>;</span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">e</span>;</span></span>

    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">e</span></span> = <span class="e Call"><span class="e Identifier"><span class="i">copysign</span></span>(<span class="n">21</span>, <span class="n">23.8</span>)</span></span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Identifier"><span class="i">e</span></span> == <span class="e Int"><span class="n">21</span></span></span>)</span>;</span>

    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">e</span></span> = <span class="e Call"><span class="e Identifier"><span class="i">copysign</span></span>(-<span class="n">21</span>, <span class="n">23.8</span>)</span></span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Identifier"><span class="i">e</span></span> == <span class="e Int"><span class="n">21</span></span></span>)</span>;</span>

    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">e</span></span> = <span class="e Call"><span class="e Identifier"><span class="i">copysign</span></span>(<span class="n">21</span>, -<span class="n">23.8</span>)</span></span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Identifier"><span class="i">e</span></span> == <span class="e Sign">-<span class="e Int"><span class="n">21</span></span></span></span>)</span>;</span>

    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">e</span></span> = <span class="e Call"><span class="e Identifier"><span class="i">copysign</span></span>(-<span class="n">21</span>, -<span class="n">23.8</span>)</span></span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Identifier"><span class="i">e</span></span> == <span class="e Sign">-<span class="e Int"><span class="n">21</span></span></span></span>)</span>;</span>

    <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">e</span></span> = <span class="e Call"><span class="e Identifier"><span class="i">copysign</span></span>(<span class="k">real</span>.<span class="i">nan</span>, -<span class="n">23.8</span>)</span></span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e AndAnd"><span class="e Call"><span class="e Identifier"><span class="i">isnan</span></span>(<span class="i">e</span>)</span> &amp;&amp; <span class="e Call"><span class="e Identifier"><span class="i">signbit</span></span>(<span class="i">e</span>)</span></span>)</span>;</span>
}</span></span></span>



<span class="bc">/******************************************
 * Creates a quiet NAN with the information from tagp[] embedded in it.
 *
 * BUGS: DMD always returns real.nan, ignoring the payload.
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">nan</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">char</span></span><span class="t Array">[]</span> <span class="i">tagp</span></span>)</span> <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">nanl</span></span></span>(<span class="i">toStringz</span>(<span class="i">tagp</span>))</span>;</span> }</span></span></span>

<span class="bc">/**
 * Calculate the next largest floating point value after x.
 *
 * Return the least number greater than x that is representable as a real;
 * thus, it gives the next point on the IEEE number line.
 *
 *  $(TABLE_SV
 *    $(SVH x,            nextUp(x)   )
 *    $(SV  -$(INFIN),    -real.max   )
 *    $(SV  $(PLUSMN)0.0, real.min*real.epsilon )
 *    $(SV  real.max,     $(INFIN) )
 *    $(SV  $(INFIN),     $(INFIN) )
 *    $(SV  $(NAN),       $(NAN)   )
 * )
 *
 * Remarks:
 * This function is included in the forthcoming IEEE 754R standard.
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">nextUp</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Alias"><span class="k">alias</span> <span class="d Variables"><span class="t TemplateInstance"><span class="i">floatTraits</span>!(<span class="o TemplateArguments"><span class="t Integral"><span class="k">real</span></span></span>)</span> <span class="i">F</span>;</span></span></span>
    <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span> == <span class="e Int"><span class="n">53</span></span></span>) <span class="s Compound">{ <span class="lc">// double</span>
        <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Identifier"><span class="i">nextUp</span></span>(<span class="k">cast</span>(<span class="k">double</span>)<span class="i">x</span>)</span>;</span>
    }</span> <span class="k">else</span> <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span>(<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>==<span class="e Int"><span class="n">113</span></span></span>) <span class="s Compound">{  <span class="lc">// quadruple</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="i">e</span> = <span class="e And"><span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span> &amp; <span class="e Index"><span class="e Paren">(<span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>)</span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span></span>;</span></span>
        <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">e</span></span> == <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span></span>) <span class="s Compound">{ <span class="lc">// NaN or Infinity</span>
             <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">x</span></span> == <span class="e Sign">-<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span></span></span>) <span class="s Return"><span class="k">return</span> <span class="e Sign">-<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">max</span></span></span>;</span></span>
             <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">x</span></span>;</span> <span class="lc">// +Inf and NaN are unchanged.</span>
        }</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span><span class="t Pointer">*</span>   <span class="i">ps</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">e</span></span></span></span>;</span></span>
        <span class="s If"><span class="k">if</span> (<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">ps</span></span>[<span class="e Identifier"><span class="i">MANTISSA_LSB</span></span>]</span> &amp; <span class="e Int"><span class="n">0x8000_0000_0000_0000</span></span></span>)  <span class="s Compound">{ <span class="lc">// Negative number</span>
            <span class="s If"><span class="k">if</span> (<span class="e AndAnd"><span class="e Equal"><span class="e Index"><span class="e Identifier"><span class="i">ps</span></span>[<span class="e Identifier"><span class="i">MANTISSA_LSB</span></span>]</span> == <span class="e Int"><span class="n">0</span></span></span>
             &amp;&amp; <span class="e Equal"><span class="e Index"><span class="e Identifier"><span class="i">ps</span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span> == <span class="e Int"><span class="n">0x8000_0000_0000_0000</span></span></span></span>) <span class="s Compound">{
                <span class="lc">// it was negative zero, change to smallest subnormal</span>
                <span class="s Expression"><span class="e Assign"><span class="e Index"><span class="e Identifier"><span class="i">ps</span></span>[<span class="e Identifier"><span class="i">MANTISSA_LSB</span></span>]</span> = <span class="e Int"><span class="n">0x0000_0000_0000_0001</span></span></span>;</span>
                <span class="s Expression"><span class="e Assign"><span class="e Index"><span class="e Identifier"><span class="i">ps</span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span> = <span class="e Int"><span class="n">0</span></span></span>;</span>
                <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">x</span></span>;</span>
            }</span></span>
            <span class="s Expression"><span class="e PreDecr">--<span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span></span>;</span>
            <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Index"><span class="e Identifier"><span class="i">ps</span></span>[<span class="e Identifier"><span class="i">MANTISSA_LSB</span></span>]</span>==<span class="e Int"><span class="n">0</span></span></span>) <span class="s Expression"><span class="e Index"><span class="e PreDecr">--<span class="e Identifier"><span class="i">ps</span></span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span>;</span></span>
        }</span> <span class="k">else</span> <span class="s Compound">{ <span class="lc">// Positive number</span>
            <span class="s Expression"><span class="e Index"><span class="e PreIncr">++<span class="e Identifier"><span class="i">ps</span></span></span>[<span class="e Identifier"><span class="i">MANTISSA_LSB</span></span>]</span>;</span>
            <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Index"><span class="e Identifier"><span class="i">ps</span></span>[<span class="e Identifier"><span class="i">MANTISSA_LSB</span></span>]</span>==<span class="e Int"><span class="n">0</span></span></span>) <span class="s Expression"><span class="e Index"><span class="e PreIncr">++<span class="e Identifier"><span class="i">ps</span></span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span>;</span></span>
        }</span></span>
        <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">x</span></span>;</span>

    }</span> <span class="k">else</span> <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span>(<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>==<span class="e Int"><span class="n">64</span></span></span>)<span class="s Compound">{ <span class="lc">// real80</span>
        <span class="lc">// For 80-bit reals, the "implied bit" is a nuisance...</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span><span class="i">pe</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span>  <span class="t Pointer">*</span><span class="i">ps</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span>  <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>

        <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">pe</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> &amp; <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span></span>)</span> == <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span></span>) <span class="s Compound">{
            <span class="lc">// First, deal with NANs and infinity</span>
            <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">x</span></span> == <span class="e Sign">-<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span></span></span>) <span class="s Return"><span class="k">return</span> <span class="e Sign">-<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">max</span></span></span>;</span></span>
            <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">x</span></span>;</span> <span class="lc">// +Inf and NaN are unchanged.</span>
        }</span></span>
        <span class="s If"><span class="k">if</span> (<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">pe</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> &amp; <span class="e Int"><span class="n">0x8000</span></span></span>)  <span class="s Compound">{
            <span class="lc">// Negative number -- need to decrease the significand</span>
            <span class="s Expression"><span class="e PreDecr">--<span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span></span>;</span>
            <span class="lc">// Need to mask with 0x7FFF... so subnormals are treated correctly.</span>
            <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Paren">(<span class="e And"><span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span> &amp; <span class="e Int"><span class="n">0x7FFF_FFFF_FFFF_FFFF</span></span></span>)</span> == <span class="e Int"><span class="n">0x7FFF_FFFF_FFFF_FFFF</span></span></span>) <span class="s Compound">{
                <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Index"><span class="e Identifier"><span class="i">pe</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> == <span class="e Int"><span class="n">0x8000</span></span></span>) <span class="s Compound">{ <span class="lc">// it was negative zero</span>
                    <span class="s Expression"><span class="e Assign"><span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span> = <span class="e Int"><span class="n">1</span></span></span>;</span>
                    <span class="s Expression"><span class="e Assign"><span class="e Index"><span class="e Identifier"><span class="i">pe</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> = <span class="e Int"><span class="n">0</span></span></span>;</span> <span class="lc">// smallest subnormal.</span>
                    <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">x</span></span>;</span>
                }</span></span>
                <span class="s Expression"><span class="e Index"><span class="e PreDecr">--<span class="e Identifier"><span class="i">pe</span></span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span>;</span>
                <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Index"><span class="e Identifier"><span class="i">pe</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> == <span class="e Int"><span class="n">0x8000</span></span></span>) <span class="s Compound">{
                    <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">x</span></span>;</span> <span class="lc">// it's become a subnormal, implied bit stays low.</span>
                }</span></span>
                <span class="s Expression"><span class="e Assign"><span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span> = <span class="e Int"><span class="n">0xFFFF_FFFF_FFFF_FFFF</span></span></span>;</span> <span class="lc">// set the implied bit</span>
                <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">x</span></span>;</span>
            }</span></span>
            <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">x</span></span>;</span>
        }</span> <span class="k">else</span> <span class="s Compound">{
            <span class="lc">// Positive number -- need to increase the significand.</span>
            <span class="lc">// Works automatically for positive zero.</span>
            <span class="s Expression"><span class="e PreIncr">++<span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span></span>;</span>
            <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Paren">(<span class="e And"><span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span> &amp; <span class="e Int"><span class="n">0x7FFF_FFFF_FFFF_FFFF</span></span></span>)</span> == <span class="e Int"><span class="n">0</span></span></span>) <span class="s Compound">{
                <span class="lc">// change in exponent</span>
                <span class="s Expression"><span class="e Index"><span class="e PreIncr">++<span class="e Identifier"><span class="i">pe</span></span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span>;</span>
                <span class="s Expression"><span class="e Assign"><span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span> = <span class="e Int"><span class="n">0x8000_0000_0000_0000</span></span></span>;</span> <span class="lc">// set the high bit</span>
            }</span></span>
        }</span></span>
        <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">x</span></span>;</span>
    }</span> <span class="k">else</span> <span class="s Compound">{ <span class="lc">// doubledouble</span>
        <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Int"><span class="n">0</span></span>, <span class="e String"><span class="sl">"Not implemented"</span></span>)</span>;</span>
    }</span></span></span></span>
}</span></span></span>

<span class="bc">/** ditto */</span>
<span class="d Function"><span class="t Integral"><span class="k">double</span></span> <span class="i">nextUp</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">double</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span><span class="i">ps</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>

    <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Paren">(<span class="e And"><span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span> &amp; <span class="e Int"><span class="n">0x7FF0_0000_0000_0000</span></span></span>)</span> == <span class="e Int"><span class="n">0x7FF0_0000_0000_0000</span></span></span>) <span class="s Compound">{
        <span class="lc">// First, deal with NANs and infinity</span>
        <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">x</span></span> == <span class="e Dot"><span class="e Sign">-<span class="e Identifier"><span class="i">x</span></span></span>.<span class="e Identifier"><span class="i">infinity</span></span></span></span>) <span class="s Return"><span class="k">return</span> <span class="e Dot"><span class="e Sign">-<span class="e Identifier"><span class="i">x</span></span></span>.<span class="e Identifier"><span class="i">max</span></span></span>;</span></span>
        <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">x</span></span>;</span> <span class="lc">// +INF and NAN are unchanged.</span>
    }</span></span>
    <span class="s If"><span class="k">if</span> (<span class="e And"><span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span> &amp; <span class="e Int"><span class="n">0x8000_0000_0000_0000</span></span></span>)  <span class="s Compound">{ <span class="lc">// Negative number</span>
        <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span> == <span class="e Int"><span class="n">0x8000_0000_0000_0000</span></span></span>) <span class="s Compound">{ <span class="lc">// it was negative zero</span>
            <span class="s Expression"><span class="e Assign"><span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span> = <span class="e Int"><span class="n">0x0000_0000_0000_0001</span></span></span>;</span> <span class="lc">// change to smallest subnormal</span>
            <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">x</span></span>;</span>
        }</span></span>
        <span class="s Expression"><span class="e PreDecr">--<span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span></span>;</span>
    }</span> <span class="k">else</span> <span class="s Compound">{ <span class="lc">// Positive number</span>
        <span class="s Expression"><span class="e PreIncr">++<span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span></span>;</span>
    }</span></span>
    <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">x</span></span>;</span>
}</span></span></span>

<span class="bc">/** ditto */</span>
<span class="d Function"><span class="t Integral"><span class="k">float</span></span> <span class="i">nextUp</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">float</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">uint</span></span> <span class="t Pointer">*</span><span class="i">ps</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">uint</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>

    <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Paren">(<span class="e And"><span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span> &amp; <span class="e Int"><span class="n">0x7F80_0000</span></span></span>)</span> == <span class="e Int"><span class="n">0x7F80_0000</span></span></span>) <span class="s Compound">{
        <span class="lc">// First, deal with NANs and infinity</span>
        <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">x</span></span> == <span class="e Dot"><span class="e Sign">-<span class="e Identifier"><span class="i">x</span></span></span>.<span class="e Identifier"><span class="i">infinity</span></span></span></span>) <span class="s Return"><span class="k">return</span> <span class="e Dot"><span class="e Sign">-<span class="e Identifier"><span class="i">x</span></span></span>.<span class="e Identifier"><span class="i">max</span></span></span>;</span></span>
        <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">x</span></span>;</span> <span class="lc">// +INF and NAN are unchanged.</span>
    }</span></span>
    <span class="s If"><span class="k">if</span> (<span class="e And"><span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span> &amp; <span class="e Int"><span class="n">0x8000_0000</span></span></span>)  <span class="s Compound">{ <span class="lc">// Negative number</span>
        <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span> == <span class="e Int"><span class="n">0x8000_0000</span></span></span>) <span class="s Compound">{ <span class="lc">// it was negative zero</span>
            <span class="s Expression"><span class="e Assign"><span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span> = <span class="e Int"><span class="n">0x0000_0001</span></span></span>;</span> <span class="lc">// change to smallest subnormal</span>
            <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">x</span></span>;</span>
        }</span></span>
        <span class="s Expression"><span class="e PreDecr">--<span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span></span>;</span>
    }</span> <span class="k">else</span> <span class="s Compound">{ <span class="lc">// Positive number</span>
        <span class="s Expression"><span class="e PreIncr">++<span class="e Deref">*<span class="e Identifier"><span class="i">ps</span></span></span></span>;</span>
    }</span></span>
    <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">x</span></span>;</span>
}</span></span></span>

<span class="bc">/**
 * Calculate the next smallest floating point value before x.
 *
 * Return the greatest number less than x that is representable as a real;
 * thus, it gives the previous point on the IEEE number line.
 *
 *  $(TABLE_SV
 *    $(SVH x,            nextDown(x)   )
 *    $(SV  $(INFIN),     real.max  )
 *    $(SV  $(PLUSMN)0.0, -real.min*real.epsilon )
 *    $(SV  -real.max,    -$(INFIN) )
 *    $(SV  -$(INFIN),    -$(INFIN) )
 *    $(SV  $(NAN),       $(NAN)    )
 * )
 *
 * Remarks:
 * This function is included in the forthcoming IEEE 754R standard.
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">nextDown</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Sign">-<span class="e Identifier"><span class="i">nextUp</span></span></span>(-<span class="i">x</span>)</span>;</span>
}</span></span></span>

<span class="bc">/** ditto */</span>
<span class="d Function"><span class="t Integral"><span class="k">double</span></span> <span class="i">nextDown</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">double</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Sign">-<span class="e Identifier"><span class="i">nextUp</span></span></span>(-<span class="i">x</span>)</span>;</span>
}</span></span></span>

<span class="bc">/** ditto */</span>
<span class="d Function"><span class="t Integral"><span class="k">float</span></span> <span class="i">nextDown</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">float</span></span> <span class="i">x</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Sign">-<span class="e Identifier"><span class="i">nextUp</span></span></span>(-<span class="i">x</span>)</span>;</span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span> <span class="s FuncBody"><span class="s Compound">{
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>( <span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">nextDown</span></span>(<span class="n">1.0</span> + <span class="k">real</span>.<span class="i">epsilon</span>)</span> == <span class="e Real"><span class="n">1.0</span></span></span>)</span>;</span>
}</span></span></span>


<span class="bc">/******************************************
 * Calculates the next representable value after x in the direction of y.
 *
 * If y &gt; x, the result will be the next largest floating-point value;
 * if y &lt; x, the result will be the next smallest value.
 * If x == y, the result is y.
 *
 * Remarks:
 * This function is not generally very useful; it's almost always better to use
 * the faster functions nextUp() or nextDown() instead.
 *
 * IEEE 754 requirements not implemented on Windows:
 * The FE_INEXACT and FE_OVERFLOW exceptions will be raised if x is finite and
 * the function result is infinite. The FE_INEXACT and FE_UNDERFLOW
 * exceptions will be raised if the function value is subnormal, and x is
 * not equal to y.
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">nextafter</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">y</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Version"><span class="k">version</span> (<span class="i">Windows</span>) <span class="s Compound">{
        <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">x</span></span>==<span class="e Identifier"><span class="i">y</span></span></span>) <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">y</span></span>;</span></span>
        <span class="s Return"><span class="k">return</span> <span class="e Cond"><span class="e Paren">(<span class="e Rel"><span class="e Identifier"><span class="i">y</span></span>&gt;<span class="e Identifier"><span class="i">x</span></span></span>)</span> ? <span class="e Call"><span class="e Identifier"><span class="i">nextUp</span></span>(<span class="i">x</span>)</span> : <span class="e Call"><span class="e Identifier"><span class="i">nextDown</span></span>(<span class="i">x</span>)</span></span>;</span>
    }</span> <span class="k">else</span> <span class="s Compound">{
        <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">nextafterl</span></span></span>(<span class="i">x</span>, <span class="i">y</span>)</span>;</span>
    }</span></span>
}</span></span></span>

<span class="lc">/// ditto</span>
<span class="d Function"><span class="t Integral"><span class="k">float</span></span> <span class="i">nextafter</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">float</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">float</span></span> <span class="i">y</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Version"><span class="k">version</span> (<span class="i">Windows</span>) <span class="s Compound">{
        <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">x</span></span>==<span class="e Identifier"><span class="i">y</span></span></span>) <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">y</span></span>;</span></span>
        <span class="s Return"><span class="k">return</span> <span class="e Cond"><span class="e Paren">(<span class="e Rel"><span class="e Identifier"><span class="i">y</span></span>&gt;<span class="e Identifier"><span class="i">x</span></span></span>)</span> ? <span class="e Call"><span class="e Identifier"><span class="i">nextUp</span></span>(<span class="i">x</span>)</span> : <span class="e Call"><span class="e Identifier"><span class="i">nextDown</span></span>(<span class="i">x</span>)</span></span>;</span>
    }</span> <span class="k">else</span> <span class="s Compound">{
        <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">nextafterf</span></span></span>(<span class="i">x</span>, <span class="i">y</span>)</span>;</span>
    }</span></span>
}</span></span></span>

<span class="lc">/// ditto</span>
<span class="d Function"><span class="t Integral"><span class="k">double</span></span> <span class="i">nextafter</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">double</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">double</span></span> <span class="i">y</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Version"><span class="k">version</span> (<span class="i">Windows</span>) <span class="s Compound">{
        <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">x</span></span>==<span class="e Identifier"><span class="i">y</span></span></span>) <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">y</span></span>;</span></span>
        <span class="s Return"><span class="k">return</span> <span class="e Cond"><span class="e Paren">(<span class="e Rel"><span class="e Identifier"><span class="i">y</span></span>&gt;<span class="e Identifier"><span class="i">x</span></span></span>)</span> ? <span class="e Call"><span class="e Identifier"><span class="i">nextUp</span></span>(<span class="i">x</span>)</span> : <span class="e Call"><span class="e Identifier"><span class="i">nextDown</span></span>(<span class="i">x</span>)</span></span>;</span>
    }</span> <span class="k">else</span> <span class="s Compound">{
        <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">nextafter</span></span></span>(<span class="i">x</span>, <span class="i">y</span>)</span>;</span>
    }</span></span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">float</span></span> <span class="i">a</span> = <span class="e Int"><span class="n">1</span></span>;</span></span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Is"><span class="k">is</span>(<span class="t Typeof"><span class="k">typeof</span>(<span class="e Call"><span class="e Identifier"><span class="i">nextafter</span></span>(<span class="i">a</span>, <span class="i">a</span>)</span>)</span> == <span class="t Integral"><span class="k">float</span></span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Rel"><span class="e Call"><span class="e Identifier"><span class="i">nextafter</span></span>(<span class="i">a</span>, <span class="i">a</span>.<span class="i">infinity</span>)</span> &gt; <span class="e Identifier"><span class="i">a</span></span></span>)</span>;</span>

    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">double</span></span> <span class="i">b</span> = <span class="e Int"><span class="n">2</span></span>;</span></span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Is"><span class="k">is</span>(<span class="t Typeof"><span class="k">typeof</span>(<span class="e Call"><span class="e Identifier"><span class="i">nextafter</span></span>(<span class="i">b</span>, <span class="i">b</span>)</span>)</span> == <span class="t Integral"><span class="k">double</span></span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Rel"><span class="e Call"><span class="e Identifier"><span class="i">nextafter</span></span>(<span class="i">b</span>, <span class="i">b</span>.<span class="i">infinity</span>)</span> &gt; <span class="e Identifier"><span class="i">b</span></span></span>)</span>;</span>

    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">c</span> = <span class="e Int"><span class="n">3</span></span>;</span></span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Is"><span class="k">is</span>(<span class="t Typeof"><span class="k">typeof</span>(<span class="e Call"><span class="e Identifier"><span class="i">nextafter</span></span>(<span class="i">c</span>, <span class="i">c</span>)</span>)</span> == <span class="t Integral"><span class="k">real</span></span>)</span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Rel"><span class="e Call"><span class="e Identifier"><span class="i">nextafter</span></span>(<span class="i">c</span>, <span class="i">c</span>.<span class="i">infinity</span>)</span> &gt; <span class="e Identifier"><span class="i">c</span></span></span>)</span>;</span>
}</span></span></span>

<span class="lc">//real nexttoward(real x, real y) { return std.c.math.nexttowardl(x, y); }</span>

<span class="bc">/*******************************************
 * Returns the positive difference between x and y.
 * Returns:
 *      $(TABLE_SV
 *      $(TR $(TH x, y)       $(TH fdim(x, y)))
 *      $(TR $(TD x $(GT) y)  $(TD x - y))
 *      $(TR $(TD x $(LT)= y) $(TD +0.0))
 *      )
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">fdim</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">y</span></span>)</span> <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Cond"><span class="e Paren">(<span class="e Rel"><span class="e Identifier"><span class="i">x</span></span> &gt; <span class="e Identifier"><span class="i">y</span></span></span>)</span> ? <span class="e Minus"><span class="e Identifier"><span class="i">x</span></span> - <span class="e Identifier"><span class="i">y</span></span></span> : <span class="e Sign">+<span class="e Real"><span class="n">0.0</span></span></span></span>;</span> }</span></span></span>

<span class="bc">/****************************************
 * Returns the larger of x and y.
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">fmax</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">y</span></span>)</span> <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Cond"><span class="e Rel"><span class="e Identifier"><span class="i">x</span></span> &gt; <span class="e Identifier"><span class="i">y</span></span></span> ? <span class="e Identifier"><span class="i">x</span></span> : <span class="e Identifier"><span class="i">y</span></span></span>;</span> }</span></span></span>

<span class="bc">/****************************************
 * Returns the smaller of x and y.
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">fmin</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">y</span></span>)</span> <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Cond"><span class="e Rel"><span class="e Identifier"><span class="i">x</span></span> &lt; <span class="e Identifier"><span class="i">y</span></span></span> ? <span class="e Identifier"><span class="i">x</span></span> : <span class="e Identifier"><span class="i">y</span></span></span>;</span> }</span></span></span>

<span class="bc">/**************************************
 * Returns (x * y) + z, rounding only once according to the
 * current rounding mode.
 *
 * BUGS: Not currently implemented - rounds twice.
 */</span>
<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">fma</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">y</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">z</span></span>)</span> <span class="s FuncBody"><span class="s Compound">{ <span class="s Return"><span class="k">return</span> <span class="e Plus"><span class="e Paren">(<span class="e Mul"><span class="e Identifier"><span class="i">x</span></span> * <span class="e Identifier"><span class="i">y</span></span></span>)</span> + <span class="e Identifier"><span class="i">z</span></span></span>;</span> }</span></span></span>

<span class="bc">/*******************************************************************
 * Fast integral powers.
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">pow</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">uint</span></span> <span class="i">n</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">p</span>;</span></span>

    <span class="s Switch"><span class="k">switch</span> (<span class="e Identifier"><span class="i">n</span></span>)
    <span class="s Compound">{
        <span class="s Case"><span class="k">case</span> <span class="e Int"><span class="n">0</span></span>:
            <span class="s Scope"><span class="s Compound"><span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">p</span></span> = <span class="e Real"><span class="n">1.0</span></span></span>;</span>
            <span class="s Break"><span class="k">break</span>;</span></span></span></span>

        <span class="s Case"><span class="k">case</span> <span class="e Int"><span class="n">1</span></span>:
            <span class="s Scope"><span class="s Compound"><span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">p</span></span> = <span class="e Identifier"><span class="i">x</span></span></span>;</span>
            <span class="s Break"><span class="k">break</span>;</span></span></span></span>

        <span class="s Case"><span class="k">case</span> <span class="e Int"><span class="n">2</span></span>:
            <span class="s Scope"><span class="s Compound"><span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">p</span></span> = <span class="e Mul"><span class="e Identifier"><span class="i">x</span></span> * <span class="e Identifier"><span class="i">x</span></span></span></span>;</span>
            <span class="s Break"><span class="k">break</span>;</span></span></span></span>

        <span class="s Default"><span class="k">default</span>:
            <span class="s Scope"><span class="s Compound"><span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">p</span></span> = <span class="e Real"><span class="n">1.0</span></span></span>;</span>
            <span class="s While"><span class="k">while</span> (<span class="e Int"><span class="n">1</span></span>)
            <span class="s Compound">{
                <span class="s If"><span class="k">if</span> (<span class="e And"><span class="e Identifier"><span class="i">n</span></span> &amp; <span class="e Int"><span class="n">1</span></span></span>)
                    <span class="s Expression"><span class="e MulAssign"><span class="e Identifier"><span class="i">p</span></span> *= <span class="e Identifier"><span class="i">x</span></span></span>;</span></span>
                <span class="s Expression"><span class="e RShiftAssign"><span class="e Identifier"><span class="i">n</span></span> &gt;&gt;= <span class="e Int"><span class="n">1</span></span></span>;</span>
                <span class="s If"><span class="k">if</span> (<span class="e Not">!<span class="e Identifier"><span class="i">n</span></span></span>)
                    <span class="s Break"><span class="k">break</span>;</span></span>
                <span class="s Expression"><span class="e MulAssign"><span class="e Identifier"><span class="i">x</span></span> *= <span class="e Identifier"><span class="i">x</span></span></span>;</span>
            }</span></span>
            <span class="s Break"><span class="k">break</span>;</span></span></span></span>
    }</span></span>
    <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">p</span></span>;</span>
}</span></span></span>

<span class="lc">/// ditto</span>

<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">pow</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">int</span></span> <span class="i">n</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">n</span></span> &lt; <span class="e Int"><span class="n">0</span></span></span>)
        <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Identifier"><span class="i">pow</span></span>(<span class="i">x</span>, <span class="k">cast</span>(<span class="k">real</span>)<span class="i">n</span>)</span>;</span>
    <span class="k">else</span>
        <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Identifier"><span class="i">pow</span></span>(<span class="i">x</span>, <span class="k">cast</span>(<span class="k">uint</span>)<span class="i">n</span>)</span>;</span></span>
}</span></span></span>

<span class="bc">/*********************************************
 * Calculates x$(SUP y).
 *
 * $(TABLE_SV
 * $(TR $(TH x) $(TH y) $(TH pow(x, y))
 *      $(TH div 0) $(TH invalid?))
 * $(TR $(TD anything)      $(TD $(PLUSMN)0.0)                $(TD 1.0)
 *      $(TD no)        $(TD no) )
 * $(TR $(TD |x| $(GT) 1)    $(TD +$(INFIN))                  $(TD +$(INFIN))
 *      $(TD no)        $(TD no) )
 * $(TR $(TD |x| $(LT) 1)    $(TD +$(INFIN))                  $(TD +0.0)
 *      $(TD no)        $(TD no) )
 * $(TR $(TD |x| $(GT) 1)    $(TD -$(INFIN))                  $(TD +0.0)
 *      $(TD no)        $(TD no) )
 * $(TR $(TD |x| $(LT) 1)    $(TD -$(INFIN))                  $(TD +$(INFIN))
 *      $(TD no)        $(TD no) )
 * $(TR $(TD +$(INFIN))      $(TD $(GT) 0.0)                  $(TD +$(INFIN))
 *      $(TD no)        $(TD no) )
 * $(TR $(TD +$(INFIN))      $(TD $(LT) 0.0)                  $(TD +0.0)
 *      $(TD no)        $(TD no) )
 * $(TR $(TD -$(INFIN))      $(TD odd integer $(GT) 0.0)      $(TD -$(INFIN))
 *      $(TD no)        $(TD no) )
 * $(TR $(TD -$(INFIN))      $(TD $(GT) 0.0, not odd integer) $(TD +$(INFIN))
 *      $(TD no)        $(TD no))
 * $(TR $(TD -$(INFIN))      $(TD odd integer $(LT) 0.0)      $(TD -0.0)
 *      $(TD no)        $(TD no) )
 * $(TR $(TD -$(INFIN))      $(TD $(LT) 0.0, not odd integer) $(TD +0.0)
 *      $(TD no)        $(TD no) )
 * $(TR $(TD $(PLUSMN)1.0)   $(TD $(PLUSMN)$(INFIN))          $(TD $(NAN))
 *      $(TD no)        $(TD yes) )
 * $(TR $(TD $(LT) 0.0)      $(TD finite, nonintegral)        $(TD $(NAN))
 *      $(TD no)        $(TD yes))
 * $(TR $(TD $(PLUSMN)0.0)   $(TD odd integer $(LT) 0.0)      $(TD $(PLUSMNINF))
 *      $(TD yes)       $(TD no) )
 * $(TR $(TD $(PLUSMN)0.0)   $(TD $(LT) 0.0, not odd integer) $(TD +$(INFIN))
 *      $(TD yes)       $(TD no))
 * $(TR $(TD $(PLUSMN)0.0)   $(TD odd integer $(GT) 0.0)      $(TD $(PLUSMN)0.0)
 *      $(TD no)        $(TD no) )
 * $(TR $(TD $(PLUSMN)0.0)   $(TD $(GT) 0.0, not odd integer) $(TD +0.0)
 *      $(TD no)        $(TD no) )
 * )
 */</span>

<span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">pow</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">y</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Version"><span class="k">version</span> (<span class="i">linux</span>) <span class="lc">// C pow() often does not handle special values correctly</span>
    <span class="s Compound">{
        <span class="s If"><span class="k">if</span> (<span class="e Call"><span class="e Identifier"><span class="i">isnan</span></span>(<span class="i">y</span>)</span>)
            <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">y</span></span>;</span></span>

        <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">y</span></span> == <span class="e Int"><span class="n">0</span></span></span>)
            <span class="s Return"><span class="k">return</span> <span class="e Int"><span class="n">1</span></span>;</span></span>           <span class="lc">// even if x is $(NAN)</span>
        <span class="s If"><span class="k">if</span> (<span class="e AndAnd"><span class="e Call"><span class="e Identifier"><span class="i">isnan</span></span>(<span class="i">x</span>)</span> &amp;&amp; <span class="e Equal"><span class="e Identifier"><span class="i">y</span></span> != <span class="e Int"><span class="n">0</span></span></span></span>)
            <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">x</span></span>;</span></span>
        <span class="s If"><span class="k">if</span> (<span class="e Call"><span class="e Identifier"><span class="i">isinf</span></span>(<span class="i">y</span>)</span>)
        <span class="s Compound">{
            <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Call"><span class="e Identifier"><span class="i">fabs</span></span>(<span class="i">x</span>)</span> &gt; <span class="e Int"><span class="n">1</span></span></span>)
            <span class="s Compound">{
                <span class="s If"><span class="k">if</span> (<span class="e Call"><span class="e Identifier"><span class="i">signbit</span></span>(<span class="i">y</span>)</span>)
                    <span class="s Return"><span class="k">return</span> <span class="e Sign">+<span class="e Real"><span class="n">0.0</span></span></span>;</span>
                <span class="k">else</span>
                    <span class="s Return"><span class="k">return</span> <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span>;</span></span>
            }</span>
            <span class="k">else</span> <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">fabs</span></span>(<span class="i">x</span>)</span> == <span class="e Int"><span class="n">1</span></span></span>)
            <span class="s Compound">{
                <span class="s Return"><span class="k">return</span> <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">nan</span></span>;</span>
            }</span>
            <span class="k">else</span> <span class="lc">// &lt; 1</span>
            <span class="s Compound">{
                <span class="s If"><span class="k">if</span> (<span class="e Call"><span class="e Identifier"><span class="i">signbit</span></span>(<span class="i">y</span>)</span>)
                    <span class="s Return"><span class="k">return</span> <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span>;</span>
                <span class="k">else</span>
                    <span class="s Return"><span class="k">return</span> <span class="e Sign">+<span class="e Real"><span class="n">0.0</span></span></span>;</span></span>
            }</span></span></span>
        }</span></span>
        <span class="s If"><span class="k">if</span> (<span class="e Call"><span class="e Identifier"><span class="i">isinf</span></span>(<span class="i">x</span>)</span>)
        <span class="s Compound">{
            <span class="s If"><span class="k">if</span> (<span class="e Call"><span class="e Identifier"><span class="i">signbit</span></span>(<span class="i">x</span>)</span>)
            <span class="s Compound">{   <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">long</span></span> <span class="i">i</span>;</span></span>

                <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">i</span></span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">long</span></span>)<span class="e Identifier"><span class="i">y</span></span></span></span>;</span>
                <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">y</span></span> &gt; <span class="e Int"><span class="n">0</span></span></span>)
                <span class="s Compound">{
                    <span class="s If"><span class="k">if</span> (<span class="e AndAnd"><span class="e Equal"><span class="e Identifier"><span class="i">i</span></span> == <span class="e Identifier"><span class="i">y</span></span></span> &amp;&amp; <span class="e And"><span class="e Identifier"><span class="i">i</span></span> &amp; <span class="e Int"><span class="n">1</span></span></span></span>)
                        <span class="s Return"><span class="k">return</span> <span class="e Sign">-<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span></span>;</span>
                    <span class="k">else</span>
                        <span class="s Return"><span class="k">return</span> <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span>;</span></span>
                }</span>
                <span class="k">else</span> <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">y</span></span> &lt; <span class="e Int"><span class="n">0</span></span></span>)
                <span class="s Compound">{
                    <span class="s If"><span class="k">if</span> (<span class="e AndAnd"><span class="e Equal"><span class="e Identifier"><span class="i">i</span></span> == <span class="e Identifier"><span class="i">y</span></span></span> &amp;&amp; <span class="e And"><span class="e Identifier"><span class="i">i</span></span> &amp; <span class="e Int"><span class="n">1</span></span></span></span>)
                        <span class="s Return"><span class="k">return</span> <span class="e Sign">-<span class="e Real"><span class="n">0.0</span></span></span>;</span>
                    <span class="k">else</span>
                        <span class="s Return"><span class="k">return</span> <span class="e Sign">+<span class="e Real"><span class="n">0.0</span></span></span>;</span></span>
                }</span></span></span>
            }</span>
            <span class="k">else</span>
            <span class="s Compound">{
                <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">y</span></span> &gt; <span class="e Int"><span class="n">0</span></span></span>)
                    <span class="s Return"><span class="k">return</span> <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span>;</span>
                <span class="k">else</span> <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">y</span></span> &lt; <span class="e Int"><span class="n">0</span></span></span>)
                    <span class="s Return"><span class="k">return</span> <span class="e Sign">+<span class="e Real"><span class="n">0.0</span></span></span>;</span></span></span>
            }</span></span>
        }</span></span>

        <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">x</span></span> == <span class="e Real"><span class="n">0.0</span></span></span>)
        <span class="s Compound">{
            <span class="s If"><span class="k">if</span> (<span class="e Call"><span class="e Identifier"><span class="i">signbit</span></span>(<span class="i">x</span>)</span>)
            <span class="s Compound">{   <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">long</span></span> <span class="i">i</span>;</span></span>

                <span class="s Expression"><span class="e Assign"><span class="e Identifier"><span class="i">i</span></span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">long</span></span>)<span class="e Identifier"><span class="i">y</span></span></span></span>;</span>
                <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">y</span></span> &gt; <span class="e Int"><span class="n">0</span></span></span>)
                <span class="s Compound">{
                    <span class="s If"><span class="k">if</span> (<span class="e AndAnd"><span class="e Equal"><span class="e Identifier"><span class="i">i</span></span> == <span class="e Identifier"><span class="i">y</span></span></span> &amp;&amp; <span class="e And"><span class="e Identifier"><span class="i">i</span></span> &amp; <span class="e Int"><span class="n">1</span></span></span></span>)
                        <span class="s Return"><span class="k">return</span> <span class="e Sign">-<span class="e Real"><span class="n">0.0</span></span></span>;</span>
                    <span class="k">else</span>
                        <span class="s Return"><span class="k">return</span> <span class="e Sign">+<span class="e Real"><span class="n">0.0</span></span></span>;</span></span>
                }</span>
                <span class="k">else</span> <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">y</span></span> &lt; <span class="e Int"><span class="n">0</span></span></span>)
                <span class="s Compound">{
                    <span class="s If"><span class="k">if</span> (<span class="e AndAnd"><span class="e Equal"><span class="e Identifier"><span class="i">i</span></span> == <span class="e Identifier"><span class="i">y</span></span></span> &amp;&amp; <span class="e And"><span class="e Identifier"><span class="i">i</span></span> &amp; <span class="e Int"><span class="n">1</span></span></span></span>)
                        <span class="s Return"><span class="k">return</span> <span class="e Sign">-<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span></span>;</span>
                    <span class="k">else</span>
                        <span class="s Return"><span class="k">return</span> <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span>;</span></span>
                }</span></span></span>
            }</span>
            <span class="k">else</span>
            <span class="s Compound">{
                <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">y</span></span> &gt; <span class="e Int"><span class="n">0</span></span></span>)
                    <span class="s Return"><span class="k">return</span> <span class="e Sign">+<span class="e Real"><span class="n">0.0</span></span></span>;</span>
                <span class="k">else</span> <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">y</span></span> &lt; <span class="e Int"><span class="n">0</span></span></span>)
                    <span class="s Return"><span class="k">return</span> <span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">infinity</span></span>;</span></span></span>
            }</span></span>
        }</span></span>
    }</span></span>
    <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Dot"><span class="e Dot"><span class="e Dot"><span class="e Identifier"><span class="i">std</span></span>.<span class="e Identifier"><span class="i">c</span></span></span>.<span class="e Identifier"><span class="i">math</span></span></span>.<span class="e Identifier"><span class="i">powl</span></span></span>(<span class="i">x</span>, <span class="i">y</span>)</span>;</span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span> = <span class="e Int"><span class="n">46</span></span>;</span></span>

    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">pow</span></span>(<span class="i">x</span>,<span class="n">0</span>)</span> == <span class="e Real"><span class="n">1.0</span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">pow</span></span>(<span class="i">x</span>,<span class="n">1</span>)</span> == <span class="e Identifier"><span class="i">x</span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">pow</span></span>(<span class="i">x</span>,<span class="n">2</span>)</span> == <span class="e Mul"><span class="e Identifier"><span class="i">x</span></span> * <span class="e Identifier"><span class="i">x</span></span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">pow</span></span>(<span class="i">x</span>,<span class="n">3</span>)</span> == <span class="e Mul"><span class="e Mul"><span class="e Identifier"><span class="i">x</span></span> * <span class="e Identifier"><span class="i">x</span></span></span> * <span class="e Identifier"><span class="i">x</span></span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">pow</span></span>(<span class="i">x</span>,<span class="n">8</span>)</span> == <span class="e Mul"><span class="e Mul"><span class="e Mul"><span class="e Paren">(<span class="e Mul"><span class="e Identifier"><span class="i">x</span></span> * <span class="e Identifier"><span class="i">x</span></span></span>)</span> * <span class="e Paren">(<span class="e Mul"><span class="e Identifier"><span class="i">x</span></span> * <span class="e Identifier"><span class="i">x</span></span></span>)</span></span> * <span class="e Paren">(<span class="e Mul"><span class="e Identifier"><span class="i">x</span></span> * <span class="e Identifier"><span class="i">x</span></span></span>)</span></span> * <span class="e Paren">(<span class="e Mul"><span class="e Identifier"><span class="i">x</span></span> * <span class="e Identifier"><span class="i">x</span></span></span>)</span></span></span>)</span>;</span>
}</span></span></span>

<span class="bc">/****************************************
 * Simple function to compare two floating point values
 * to a specified precision.
 * Returns:
 *      1       match
 *      0       nomatch
 */</span>

<span class="d Protection"><span class="k">private</span> <span class="d Function"><span class="t Integral"><span class="k">int</span></span> <span class="i">mfeq</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">y</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">precision</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">x</span></span> == <span class="e Identifier"><span class="i">y</span></span></span>)
        <span class="s Return"><span class="k">return</span> <span class="e Int"><span class="n">1</span></span>;</span></span>
    <span class="s If"><span class="k">if</span> (<span class="e Call"><span class="e Identifier"><span class="i">isnan</span></span>(<span class="i">x</span>)</span>)
        <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Identifier"><span class="i">isnan</span></span>(<span class="i">y</span>)</span>;</span></span>
    <span class="s If"><span class="k">if</span> (<span class="e Call"><span class="e Identifier"><span class="i">isnan</span></span>(<span class="i">y</span>)</span>)
        <span class="s Return"><span class="k">return</span> <span class="e Int"><span class="n">0</span></span>;</span></span>
    <span class="s Return"><span class="k">return</span> <span class="e Rel"><span class="e Call"><span class="e Identifier"><span class="i">fabs</span></span>(<span class="i">x</span> - <span class="i">y</span>)</span> &lt;= <span class="e Identifier"><span class="i">precision</span></span></span>;</span>
}</span></span></span></span>

<span class="bc">/**************************************
 * To what precision is x equal to y?
 *
 * Returns: the number of mantissa bits which are equal in x and y.
 * eg, 0x1.F8p+60 and 0x1.F1p+60 are equal to 5 bits of precision.
 *
 *      $(TABLE_SV
 *      $(TR $(TH x)      $(TH y)          $(TH feqrel(x, y)))
 *      $(TR $(TD x)      $(TD x)          $(TD real.mant_dig))
 *      $(TR $(TD x)      $(TD $(GT)= 2*x) $(TD 0))
 *      $(TR $(TD x)      $(TD $(LT)= x/2) $(TD 0))
 *      $(TR $(TD $(NAN)) $(TD any)        $(TD 0))
 *      $(TR $(TD any)    $(TD $(NAN))     $(TD 0))
 *      )
 */</span>
<span class="d Template"><span class="d Compound"><span class="d Function"><span class="t Integral"><span class="k">int</span></span> <span class="i">feqrel</span><span class="o TemplateParameters">(<span class="o TemplateTypeParameter"><span class="i">X</span></span>)</span><span class="o Parameters">(<span class="o Parameter"><span class="t Identifier"><span class="i">X</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Identifier"><span class="i">X</span></span> <span class="i">y</span></span>)</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="bc">/* Public Domain. Author: Don Clugston, 18 Aug 2005.
     */</span>
  <span class="s StaticAssert"><span class="k">static</span> <span class="k">assert</span>(<span class="e OrOr"><span class="e OrOr"><span class="e Is"><span class="k">is</span>(<span class="t Identifier"><span class="i">X</span></span>==<span class="t Integral"><span class="k">real</span></span>)</span> || <span class="e Is"><span class="k">is</span>(<span class="t Identifier"><span class="i">X</span></span>==<span class="t Integral"><span class="k">double</span></span>)</span></span> || <span class="e Is"><span class="k">is</span>(<span class="t Identifier"><span class="i">X</span></span>==<span class="t Integral"><span class="k">float</span></span>)</span></span>,
        <span class="e String"><span class="sl">"Only float, double, and real are supported by feqrel"</span></span>);</span>

  <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e Dot"><span class="e Identifier"><span class="i">X</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span> == <span class="e Int"><span class="n">106</span></span></span>) <span class="s Compound">{ <span class="lc">// doubledouble.</span>
     <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Index"><span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">double</span></span><span class="t Pointer">*</span>)<span class="e Paren">(<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span>)</span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span> == <span class="e Index"><span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">double</span></span><span class="t Pointer">*</span>)<span class="e Paren">(<span class="e Address">&amp;<span class="e Identifier"><span class="i">y</span></span></span>)</span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span></span>) <span class="s Compound">{
         <span class="s Return"><span class="k">return</span> <span class="e Plus"><span class="e TypeDotId"><span class="t Integral"><span class="k">double</span></span>.<span class="i">mant_dig</span></span>
         + <span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="k">cast</span>(<span class="k">double</span>*)(&amp;<span class="i">x</span>)[<span class="i">MANTISSA_LSB</span>],
                  <span class="k">cast</span>(<span class="k">double</span>*)(&amp;<span class="i">y</span>)[<span class="i">MANTISSA_LSB</span>])</span></span>;</span>
     }</span> <span class="k">else</span> <span class="s Compound">{
         <span class="s Return"><span class="k">return</span> <span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="k">cast</span>(<span class="k">double</span>*)(&amp;<span class="i">x</span>)[<span class="i">MANTISSA_MSB</span>],
                       <span class="k">cast</span>(<span class="k">double</span>*)(&amp;<span class="i">y</span>)[<span class="i">MANTISSA_MSB</span>])</span>;</span>
     }</span></span>
  }</span> <span class="k">else</span> <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e OrOr"><span class="e OrOr"><span class="e Equal"><span class="e Dot"><span class="e Identifier"><span class="i">X</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span>==<span class="e Int"><span class="n">64</span></span></span> || <span class="e Equal"><span class="e Dot"><span class="e Identifier"><span class="i">X</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span>==<span class="e Int"><span class="n">113</span></span></span></span> || <span class="e Equal"><span class="e Dot"><span class="e Identifier"><span class="i">X</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span>==<span class="e Int"><span class="n">53</span></span></span></span>) <span class="s Compound">{

    <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">x</span></span> == <span class="e Identifier"><span class="i">y</span></span></span>) <span class="s Return"><span class="k">return</span> <span class="e Dot"><span class="e Identifier"><span class="i">X</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span>;</span></span> <span class="lc">// ensure diff!=0, cope with INF.</span>

    <span class="s Declaration"><span class="d Variables"><span class="t Identifier"><span class="i">X</span></span> <span class="i">diff</span> = <span class="e Call"><span class="e Identifier"><span class="i">fabs</span></span>(<span class="i">x</span> - <span class="i">y</span>)</span>;</span></span>

    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span><span class="i">pa</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span>)<span class="e Paren">(<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span>)</span></span>;</span></span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span><span class="i">pb</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span>)<span class="e Paren">(<span class="e Address">&amp;<span class="e Identifier"><span class="i">y</span></span></span>)</span></span>;</span></span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span><span class="i">pd</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span>)<span class="e Paren">(<span class="e Address">&amp;<span class="e Identifier"><span class="i">diff</span></span></span>)</span></span>;</span></span>

    <span class="s Declaration"><span class="d Alias"><span class="k">alias</span> <span class="d Variables"><span class="t TemplateInstance"><span class="i">floatTraits</span>!(<span class="o TemplateArguments"><span class="t Identifier"><span class="i">X</span></span></span>)</span> <span class="i">F</span>;</span></span></span>

    <span class="lc">// The difference in abs(exponent) between x or y and abs(x-y)</span>
    <span class="lc">// is equal to the number of significand bits of x which are</span>
    <span class="lc">// equal to y. If negative, x and y have different exponents.</span>
    <span class="lc">// If positive, x and y are equal to 'bitsdiff' bits.</span>
    <span class="lc">// AND with 0x7FFF to form the absolute value.</span>
    <span class="lc">// To avoid out-by-1 errors, we subtract 1 so it rounds down</span>
    <span class="lc">// if the exponents were different. This means 'bitsdiff' is</span>
    <span class="lc">// always 1 lower than we want, except that if bitsdiff==0,</span>
    <span class="lc">// they could have 0 or 1 bits in common.</span>

 <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e OrOr"><span class="e Equal"><span class="e Dot"><span class="e Identifier"><span class="i">X</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span>==<span class="e Int"><span class="n">64</span></span></span> || <span class="e Equal"><span class="e Dot"><span class="e Identifier"><span class="i">X</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span>==<span class="e Int"><span class="n">113</span></span></span></span>) <span class="s Compound">{ <span class="lc">// real80 or quadruple</span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">int</span></span> <span class="i">bitsdiff</span> = <span class="e Minus"><span class="e Paren">( <span class="e RShift"><span class="e Paren">(<span class="e Minus"><span class="e Plus"><span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">pa</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span>&amp;<span class="e Int"><span class="n">0x7FFF</span></span></span>)</span>
                    + <span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">pb</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span>&amp;<span class="e Int"><span class="n">0x7FFF</span></span></span>)</span></span>-<span class="e Int"><span class="n">1</span></span></span>)</span>&gt;&gt;<span class="e Int"><span class="n">1</span></span></span>)</span>
                    - <span class="e Index"><span class="e Identifier"><span class="i">pd</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span></span>;</span></span>
 }</span> <span class="k">else</span> <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e Dot"><span class="e Identifier"><span class="i">X</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span>==<span class="e Int"><span class="n">53</span></span></span>) <span class="s Compound">{ <span class="lc">// double</span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">int</span></span> <span class="i">bitsdiff</span> = <span class="e RShift"><span class="e Paren">(<span class="e Minus"><span class="e Paren">( <span class="e RShift"><span class="e Paren">(<span class="e Minus"><span class="e Plus"><span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">pa</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span>&amp;<span class="e Int"><span class="n">0x7FF0</span></span></span>)</span>
                     + <span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">pb</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span>&amp;<span class="e Int"><span class="n">0x7FF0</span></span></span>)</span></span>-<span class="e Int"><span class="n">0x10</span></span></span>)</span>&gt;&gt;<span class="e Int"><span class="n">1</span></span></span>)</span>
                     - <span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">pd</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span>&amp;<span class="e Int"><span class="n">0x7FF0</span></span></span>)</span></span>)</span>&gt;&gt;<span class="e Int"><span class="n">4</span></span></span>;</span></span>
 }</span></span></span>
    <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Index"><span class="e Identifier"><span class="i">pd</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> == <span class="e Int"><span class="n">0</span></span></span>)
    <span class="s Compound">{   <span class="lc">// Difference is denormal</span>
        <span class="lc">// For denormals, we need to add the number of zeros that</span>
        <span class="lc">// lie at the start of diff's significand.</span>
        <span class="lc">// We do this by multiplying by 2^real.mant_dig</span>
        <span class="s Expression"><span class="e MulAssign"><span class="e Identifier"><span class="i">diff</span></span> *= <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">POW2MANTDIG</span></span></span></span>;</span>
        <span class="s Return"><span class="k">return</span> <span class="e Minus"><span class="e Plus"><span class="e Identifier"><span class="i">bitsdiff</span></span> + <span class="e Dot"><span class="e Identifier"><span class="i">X</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span></span> - <span class="e Index"><span class="e Identifier"><span class="i">pd</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span></span>;</span>
    }</span></span>

    <span class="s If"><span class="k">if</span> (<span class="e Rel"><span class="e Identifier"><span class="i">bitsdiff</span></span> &gt; <span class="e Int"><span class="n">0</span></span></span>)
        <span class="s Return"><span class="k">return</span> <span class="e Plus"><span class="e Identifier"><span class="i">bitsdiff</span></span> + <span class="e Int"><span class="n">1</span></span></span>;</span></span> <span class="lc">// add the 1 we subtracted before</span>

    <span class="lc">// Avoid out-by-1 errors when factor is almost 2.</span>
     <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e OrOr"><span class="e Equal"><span class="e Dot"><span class="e Identifier"><span class="i">X</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span>==<span class="e Int"><span class="n">64</span></span></span> || <span class="e Equal"><span class="e Dot"><span class="e Identifier"><span class="i">X</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span>==<span class="e Int"><span class="n">113</span></span></span></span>) <span class="s Compound">{ <span class="lc">// real80 or quadruple</span>
        <span class="s Return"><span class="k">return</span> <span class="e Cond"><span class="e Paren">(<span class="e Equal"><span class="e Identifier"><span class="i">bitsdiff</span></span> == <span class="e Int"><span class="n">0</span></span></span>)</span> ? <span class="e Paren">(<span class="e Equal"><span class="e Index"><span class="e Identifier"><span class="i">pa</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> == <span class="e Index"><span class="e Identifier"><span class="i">pb</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span></span>)</span> : <span class="e Int"><span class="n">0</span></span></span>;</span>
     }</span> <span class="k">else</span> <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e Dot"><span class="e Identifier"><span class="i">X</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span>==<span class="e Int"><span class="n">53</span></span></span>) <span class="s Compound">{ <span class="lc">// double</span>
        <span class="s If"><span class="k">if</span> (<span class="e AndAnd"><span class="e Equal"><span class="e Identifier"><span class="i">bitsdiff</span></span> == <span class="e Int"><span class="n">0</span></span></span>
          &amp;&amp; <span class="e Not">!<span class="e Paren">(<span class="e And"><span class="e Paren">(<span class="e Xor"><span class="e Index"><span class="e Identifier"><span class="i">pa</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> ^ <span class="e Index"><span class="e Identifier"><span class="i">pb</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span></span>)</span>&amp; <span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPMASK</span></span></span></span>)</span></span></span>) <span class="s Compound">{
              <span class="s Return"><span class="k">return</span> <span class="e Int"><span class="n">1</span></span>;</span>
        }</span> <span class="k">else</span> <span class="s Return"><span class="k">return</span> <span class="e Int"><span class="n">0</span></span>;</span></span>
     }</span></span></span>
 }</span> <span class="k">else</span> <span class="s Compound">{
    <span class="s Throw"><span class="k">throw</span> <span class="e New"><span class="k">new</span> <span class="t Identifier"><span class="i">NotImplemented</span></span>(<span class="e String"><span class="sl">"feqrel"</span></span>)</span>;</span>
 }</span></span></span>
}</span></span></span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
   <span class="lc">// Exact equality</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="k">real</span>.<span class="i">max</span>,<span class="k">real</span>.<span class="i">max</span>)</span>==<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span></span>)</span>;</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="n">0.0L</span>,<span class="n">0.0L</span>)</span>==<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span></span>)</span>;</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="n">7.1824L</span>,<span class="n">7.1824L</span>)</span>==<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span></span>)</span>;</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="k">real</span>.<span class="i">infinity</span>,<span class="k">real</span>.<span class="i">infinity</span>)</span>==<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span></span>)</span>;</span>

   <span class="lc">// a few bits away from exact equality</span>
   <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">w</span>=<span class="e Int"><span class="n">1</span></span>;</span></span>
   <span class="s For"><span class="k">for</span> (<span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">int</span></span> <span class="i">i</span>=<span class="e Int"><span class="n">1</span></span>;</span></span> <span class="e Rel"><span class="e Identifier"><span class="i">i</span></span>&lt;<span class="e Minus"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>-<span class="e Int"><span class="n">1</span></span></span></span>; <span class="e PreIncr">++<span class="e Identifier"><span class="i">i</span></span></span>) <span class="s Compound">{
      <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="n">1</span>+<span class="i">w</span>*<span class="k">real</span>.<span class="i">epsilon</span>,<span class="n">1.0L</span>)</span>==<span class="e Minus"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>-<span class="e Identifier"><span class="i">i</span></span></span></span>)</span>;</span>
      <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="n">1</span>-<span class="i">w</span>*<span class="k">real</span>.<span class="i">epsilon</span>,<span class="n">1.0L</span>)</span>==<span class="e Minus"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>-<span class="e Identifier"><span class="i">i</span></span></span></span>)</span>;</span>
      <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="n">1.0L</span>,<span class="n">1</span>+(<span class="i">w</span>-<span class="n">1</span>)*<span class="k">real</span>.<span class="i">epsilon</span>)</span>==<span class="e Plus"><span class="e Minus"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>-<span class="e Identifier"><span class="i">i</span></span></span>+<span class="e Int"><span class="n">1</span></span></span></span>)</span>;</span>
      <span class="s Expression"><span class="e MulAssign"><span class="e Identifier"><span class="i">w</span></span>*=<span class="e Int"><span class="n">2</span></span></span>;</span>
   }</span></span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="n">1.5</span>+<span class="k">real</span>.<span class="i">epsilon</span>,<span class="n">1.5L</span>)</span>==<span class="e Minus"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>-<span class="e Int"><span class="n">1</span></span></span></span>)</span>;</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="n">1.5</span>-<span class="k">real</span>.<span class="i">epsilon</span>,<span class="n">1.5L</span>)</span>==<span class="e Minus"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>-<span class="e Int"><span class="n">1</span></span></span></span>)</span>;</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="n">1.5</span>-<span class="k">real</span>.<span class="i">epsilon</span>,<span class="n">1.5</span>+<span class="k">real</span>.<span class="i">epsilon</span>)</span>==<span class="e Minus"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>-<span class="e Int"><span class="n">2</span></span></span></span>)</span>;</span>

   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="k">real</span>.<span class="i">min</span>/<span class="n">8</span>,<span class="k">real</span>.<span class="i">min</span>/<span class="n">17</span>)</span>==<span class="e Int"><span class="n">3</span></span></span>)</span>;</span><span class="s Empty">;</span>

   <span class="lc">// Numbers that are close</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="n">0x1.Bp+84</span>, <span class="n">0x1.B8p+84</span>)</span>==<span class="e Int"><span class="n">5</span></span></span>)</span>;</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="n">0x1.8p+10</span>, <span class="n">0x1.Cp+10</span>)</span>==<span class="e Int"><span class="n">2</span></span></span>)</span>;</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="n">1.5</span>*(<span class="n">1</span>-<span class="k">real</span>.<span class="i">epsilon</span>), <span class="n">1.0L</span>)</span>==<span class="e Int"><span class="n">2</span></span></span>)</span>;</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="n">1.5</span>, <span class="n">1.0</span>)</span>==<span class="e Int"><span class="n">1</span></span></span>)</span>;</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="n">2</span>*(<span class="n">1</span>-<span class="k">real</span>.<span class="i">epsilon</span>), <span class="n">1.0L</span>)</span>==<span class="e Int"><span class="n">1</span></span></span>)</span>;</span>

   <span class="lc">// Factors of 2</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="k">real</span>.<span class="i">max</span>,<span class="k">real</span>.<span class="i">infinity</span>)</span>==<span class="e Int"><span class="n">0</span></span></span>)</span>;</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="n">2</span>*(<span class="n">1</span>-<span class="k">real</span>.<span class="i">epsilon</span>), <span class="n">1.0L</span>)</span>==<span class="e Int"><span class="n">1</span></span></span>)</span>;</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="n">1.0</span>, <span class="n">2.0</span>)</span>==<span class="e Int"><span class="n">0</span></span></span>)</span>;</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="n">4.0</span>, <span class="n">1.0</span>)</span>==<span class="e Int"><span class="n">0</span></span></span>)</span>;</span>

   <span class="lc">// Extreme inequality</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="k">real</span>.<span class="i">nan</span>,<span class="k">real</span>.<span class="i">nan</span>)</span>==<span class="e Int"><span class="n">0</span></span></span>)</span>;</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="n">0.0L</span>,-<span class="k">real</span>.<span class="i">nan</span>)</span>==<span class="e Int"><span class="n">0</span></span></span>)</span>;</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="k">real</span>.<span class="i">nan</span>,<span class="k">real</span>.<span class="i">infinity</span>)</span>==<span class="e Int"><span class="n">0</span></span></span>)</span>;</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="k">real</span>.<span class="i">infinity</span>,-<span class="k">real</span>.<span class="i">infinity</span>)</span>==<span class="e Int"><span class="n">0</span></span></span>)</span>;</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(-<span class="k">real</span>.<span class="i">max</span>,<span class="k">real</span>.<span class="i">infinity</span>)</span>==<span class="e Int"><span class="n">0</span></span></span>)</span>;</span>
   <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">feqrel</span></span>(<span class="k">real</span>.<span class="i">max</span>,-<span class="k">real</span>.<span class="i">max</span>)</span>==<span class="e Int"><span class="n">0</span></span></span>)</span>;</span>
}</span></span></span>

<span class="d Protection"><span class="k">package</span>: <span class="lc">// Not public yet</span>
<span class="bc">/* Return the value that lies halfway between x and y on the IEEE number line.
 *
 * Formally, the result is the arithmetic mean of the binary significands of x
 * and y, multiplied by the geometric mean of the binary exponents of x and y.
 * x and y must have the same sign, and must not be NaN.
 * Note: this function is useful for ensuring O(log n) behaviour in algorithms
 * involving a 'binary chop'.
 *
 * Special cases:
 * If x and y are within a factor of 2, (ie, feqrel(x, y) &gt; 0), the return value
 * is the arithmetic mean (x + y) / 2.
 * If x and y are even powers of 2, the return value is the geometric mean,
 *   ieeeMean(x, y) = sqrt(x * y).
 *
 */</span>
<span class="d Compound"><span class="d Template"><span class="d Compound"><span class="d Function"><span class="t Identifier"><span class="i">T</span></span> <span class="i">ieeeMean</span><span class="o TemplateParameters">(<span class="o TemplateTypeParameter"><span class="i">T</span></span>)</span><span class="o Parameters">(<span class="o Parameter"><span class="t Identifier"><span class="i">T</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Identifier"><span class="i">T</span></span> <span class="i">y</span></span>)</span>
<span class="s FuncBody"><span class="k">in</span> <span class="s Compound">{
    <span class="lc">// both x and y must have the same sign, and must not be NaN.</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">signbit</span></span>(<span class="i">x</span>)</span> == <span class="e Call"><span class="e Identifier"><span class="i">signbit</span></span>(<span class="i">y</span>)</span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e AndAnd"><span class="e Rel"><span class="e Identifier"><span class="i">x</span></span>&lt;&gt;=<span class="e Int"><span class="n">0</span></span></span> &amp;&amp; <span class="e Rel"><span class="e Identifier"><span class="i">y</span></span>&lt;&gt;=<span class="e Int"><span class="n">0</span></span></span></span>)</span>;</span>
}</span>
<span class="k">body</span> <span class="s Compound">{
    <span class="lc">// Runtime behaviour for contract violation:</span>
    <span class="lc">// If signs are opposite, or one is a NaN, return 0.</span>
    <span class="s If"><span class="k">if</span> (<span class="e Not">!<span class="e Paren">(<span class="e OrOr"><span class="e Paren">(<span class="e AndAnd"><span class="e Rel"><span class="e Identifier"><span class="i">x</span></span>&gt;=<span class="e Int"><span class="n">0</span></span></span> &amp;&amp; <span class="e Rel"><span class="e Identifier"><span class="i">y</span></span>&gt;=<span class="e Int"><span class="n">0</span></span></span></span>)</span> || <span class="e Paren">(<span class="e AndAnd"><span class="e Rel"><span class="e Identifier"><span class="i">x</span></span>&lt;=<span class="e Int"><span class="n">0</span></span></span> &amp;&amp; <span class="e Rel"><span class="e Identifier"><span class="i">y</span></span>&lt;=<span class="e Int"><span class="n">0</span></span></span></span>)</span></span>)</span></span>) <span class="s Return"><span class="k">return</span> <span class="e Real"><span class="n">0.0</span></span>;</span></span>

    <span class="lc">// The implementation is simple: cast x and y to integers,</span>
    <span class="lc">// average them (avoiding overflow), and cast the result back to a floating-point number.</span>

    <span class="s Declaration"><span class="d Alias"><span class="k">alias</span> <span class="d Variables"><span class="t TemplateInstance"><span class="i">floatTraits</span>!(<span class="o TemplateArguments"><span class="t Integral"><span class="k">real</span></span></span>)</span> <span class="i">F</span>;</span></span></span>
    <span class="s Declaration"><span class="d Variables"><span class="t Identifier"><span class="i">T</span></span> <span class="i">u</span>;</span></span>
    <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e Dot"><span class="e Identifier"><span class="i">T</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span>==<span class="e Int"><span class="n">64</span></span></span>) <span class="s Compound">{ <span class="lc">// real80</span>
        <span class="lc">// There's slight additional complexity because they are actually</span>
        <span class="lc">// 79-bit reals...</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span><span class="i">ue</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">u</span></span></span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span><span class="i">ul</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">u</span></span></span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span><span class="i">xe</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span><span class="i">xl</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span><span class="i">ye</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">y</span></span></span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span><span class="i">yl</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">y</span></span></span></span>;</span></span>
        <span class="lc">// Ignore the useless implicit bit. (Bonus: this prevents overflows)</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span> <span class="i">m</span> = <span class="e Plus"><span class="e Paren">(<span class="e And"><span class="e Paren">(<span class="e Deref">*<span class="e Identifier"><span class="i">xl</span></span></span>)</span> &amp; <span class="e Int"><span class="n">0x7FFF_FFFF_FFFF_FFFFL</span></span></span>)</span> + <span class="e Paren">(<span class="e And"><span class="e Paren">(<span class="e Deref">*<span class="e Identifier"><span class="i">yl</span></span></span>)</span> &amp; <span class="e Int"><span class="n">0x7FFF_FFFF_FFFF_FFFFL</span></span></span>)</span></span>;</span></span>

        <span class="lc">// Avoid ridiculous warning</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ushort</span></span> <span class="i">e</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span>)<span class="e Paren">(<span class="e Plus"><span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">xe</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> &amp; <span class="e Int"><span class="n">0x7FFF</span></span></span>)</span>
                              + <span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">ye</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span> &amp; <span class="e Int"><span class="n">0x7FFF</span></span></span>)</span></span>)</span></span>;</span></span>
        <span class="s If"><span class="k">if</span> (<span class="e And"><span class="e Identifier"><span class="i">m</span></span> &amp; <span class="e Int"><span class="n">0x8000_0000_0000_0000L</span></span></span>) <span class="s Compound">{
            <span class="s Expression"><span class="e PreIncr">++<span class="e Identifier"><span class="i">e</span></span></span>;</span>
            <span class="s Expression"><span class="e AndAssign"><span class="e Identifier"><span class="i">m</span></span> &amp;= <span class="e Int"><span class="n">0x7FFF_FFFF_FFFF_FFFFL</span></span></span>;</span>
        }</span></span>
        <span class="lc">// Now do a multi-byte right shift</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">uint</span></span> <span class="i">c</span> = <span class="e And"><span class="e Identifier"><span class="i">e</span></span> &amp; <span class="e Int"><span class="n">1</span></span></span>;</span></span> <span class="lc">// carry</span>
        <span class="s Expression"><span class="e RShiftAssign"><span class="e Identifier"><span class="i">e</span></span> &gt;&gt;= <span class="e Int"><span class="n">1</span></span></span>;</span>
        <span class="s Expression"><span class="e URShiftAssign"><span class="e Identifier"><span class="i">m</span></span> &gt;&gt;&gt;= <span class="e Int"><span class="n">1</span></span></span>;</span>
        <span class="s If"><span class="k">if</span> (<span class="e Identifier"><span class="i">c</span></span>) <span class="s Expression"><span class="e OrAssign"><span class="e Identifier"><span class="i">m</span></span> |= <span class="e Int"><span class="n">0x4000_0000_0000_0000L</span></span></span>;</span></span> <span class="lc">// shift carry into significand</span>
        <span class="s If"><span class="k">if</span> (<span class="e Identifier"><span class="i">e</span></span>) <span class="s Expression"><span class="e Assign"><span class="e Deref">*<span class="e Identifier"><span class="i">ul</span></span></span> = <span class="e Or"><span class="e Identifier"><span class="i">m</span></span> | <span class="e Int"><span class="n">0x8000_0000_0000_0000L</span></span></span></span>;</span> <span class="lc">// set implicit bit...</span>
        <span class="k">else</span> <span class="s Expression"><span class="e Assign"><span class="e Deref">*<span class="e Identifier"><span class="i">ul</span></span></span> = <span class="e Identifier"><span class="i">m</span></span></span>;</span></span> <span class="lc">// ... unless exponent is 0 (denormal or zero).</span>
        <span class="lc">// Avoid ridiculous warning</span>
        <span class="s Expression"><span class="e Assign"><span class="e Index"><span class="e Identifier"><span class="i">ue</span></span>[<span class="e Int"><span class="n">4</span></span>]</span>= <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ushort</span></span>)<span class="e Paren">( <span class="e Or"><span class="e Identifier"><span class="i">e</span></span> | <span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">xe</span></span>[<span class="e Dot"><span class="e Identifier"><span class="i">F</span></span>.<span class="e Identifier"><span class="i">EXPPOS_SHORT</span></span></span>]</span>&amp; <span class="e Int"><span class="n">0x8000</span></span></span>)</span></span>)</span></span></span>;</span> <span class="lc">// restore sign bit</span>
    }</span> <span class="k">else</span> <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span>(<span class="e Equal"><span class="e Dot"><span class="e Identifier"><span class="i">T</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span> == <span class="e Int"><span class="n">113</span></span></span>) <span class="s Compound">{ <span class="lc">//quadruple</span>
        <span class="lc">// This would be trivial if 'ucent' were implemented...</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span><span class="i">ul</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">u</span></span></span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span><span class="i">xl</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span><span class="i">yl</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">y</span></span></span></span>;</span></span>
        <span class="lc">// Multi-byte add, then multi-byte right shift.</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span> <span class="i">mh</span> = <span class="e Paren">(<span class="e Plus"><span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">xl</span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span> &amp; <span class="e Int"><span class="n">0x7FFF_FFFF_FFFF_FFFFL</span></span></span>)</span>
                  + <span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">yl</span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span> &amp; <span class="e Int"><span class="n">0x7FFF_FFFF_FFFF_FFFFL</span></span></span>)</span></span>)</span>;</span></span>
        <span class="lc">// Discard the lowest bit (to avoid overflow)</span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span> <span class="i">ml</span> = <span class="e Plus"><span class="e Paren">(<span class="e URShift"><span class="e Index"><span class="e Identifier"><span class="i">xl</span></span>[<span class="e Identifier"><span class="i">MANTISSA_LSB</span></span>]</span>&gt;&gt;&gt;<span class="e Int"><span class="n">1</span></span></span>)</span> + <span class="e Paren">(<span class="e URShift"><span class="e Index"><span class="e Identifier"><span class="i">yl</span></span>[<span class="e Identifier"><span class="i">MANTISSA_LSB</span></span>]</span>&gt;&gt;&gt;<span class="e Int"><span class="n">1</span></span></span>)</span></span>;</span></span>
        <span class="lc">// add the lowest bit back in, if necessary.</span>
        <span class="s If"><span class="k">if</span> (<span class="e And"><span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">xl</span></span>[<span class="e Identifier"><span class="i">MANTISSA_LSB</span></span>]</span> &amp; <span class="e Index"><span class="e Identifier"><span class="i">yl</span></span>[<span class="e Identifier"><span class="i">MANTISSA_LSB</span></span>]</span></span> &amp; <span class="e Int"><span class="n">1</span></span></span>) <span class="s Compound">{
            <span class="s Expression"><span class="e PreIncr">++<span class="e Identifier"><span class="i">ml</span></span></span>;</span>
            <span class="s If"><span class="k">if</span> (<span class="e Equal"><span class="e Identifier"><span class="i">ml</span></span>==<span class="e Int"><span class="n">0</span></span></span>) <span class="s Expression"><span class="e PreIncr">++<span class="e Identifier"><span class="i">mh</span></span></span>;</span></span>
        }</span></span>
        <span class="s Expression"><span class="e URShiftAssign"><span class="e Identifier"><span class="i">mh</span></span> &gt;&gt;&gt;=<span class="e Int"><span class="n">1</span></span></span>;</span>
        <span class="s Expression"><span class="e Assign"><span class="e Index"><span class="e Identifier"><span class="i">ul</span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span> = <span class="e Or"><span class="e Identifier"><span class="i">mh</span></span> | <span class="e Paren">(<span class="e And"><span class="e Index"><span class="e Identifier"><span class="i">xl</span></span>[<span class="e Identifier"><span class="i">MANTISSA_MSB</span></span>]</span> &amp; <span class="e Int"><span class="n">0x8000_0000_0000_0000</span></span></span>)</span></span></span>;</span>
        <span class="s Expression"><span class="e Assign"><span class="e Index"><span class="e Identifier"><span class="i">ul</span></span>[<span class="e Identifier"><span class="i">MANTISSA_LSB</span></span>]</span> = <span class="e Identifier"><span class="i">ml</span></span></span>;</span>
    }</span> <span class="k">else</span> <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e Dot"><span class="e Identifier"><span class="i">T</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span> == <span class="e TypeDotId"><span class="t Integral"><span class="k">double</span></span>.<span class="i">mant_dig</span></span></span>) <span class="s Compound">{
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span><span class="i">ul</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">u</span></span></span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span><span class="i">xl</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span><span class="i">yl</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">ulong</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">y</span></span></span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">ulong</span></span> <span class="i">m</span> = <span class="e URShift"><span class="e Paren">(<span class="e Plus"><span class="e Paren">(<span class="e And"><span class="e Paren">(<span class="e Deref">*<span class="e Identifier"><span class="i">xl</span></span></span>)</span> &amp; <span class="e Int"><span class="n">0x7FFF_FFFF_FFFF_FFFFL</span></span></span>)</span>
                 + <span class="e Paren">(<span class="e And"><span class="e Paren">(<span class="e Deref">*<span class="e Identifier"><span class="i">yl</span></span></span>)</span> &amp; <span class="e Int"><span class="n">0x7FFF_FFFF_FFFF_FFFFL</span></span></span>)</span></span>)</span> &gt;&gt;&gt; <span class="e Int"><span class="n">1</span></span></span>;</span></span>
        <span class="s Expression"><span class="e OrAssign"><span class="e Identifier"><span class="i">m</span></span> |= <span class="e Paren">(<span class="e And"><span class="e Paren">(<span class="e Deref">*<span class="e Identifier"><span class="i">xl</span></span></span>)</span> &amp; <span class="e Int"><span class="n">0x8000_0000_0000_0000L</span></span></span>)</span></span>;</span>
        <span class="s Expression"><span class="e Assign"><span class="e Deref">*<span class="e Identifier"><span class="i">ul</span></span></span> = <span class="e Identifier"><span class="i">m</span></span></span>;</span>
    }</span> <span class="k">else</span> <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e Dot"><span class="e Identifier"><span class="i">T</span></span>.<span class="e Identifier"><span class="i">mant_dig</span></span></span> == <span class="e TypeDotId"><span class="t Integral"><span class="k">float</span></span>.<span class="i">mant_dig</span></span></span>) <span class="s Compound">{
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">uint</span></span> <span class="t Pointer">*</span><span class="i">ul</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">uint</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">u</span></span></span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">uint</span></span> <span class="t Pointer">*</span><span class="i">xl</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">uint</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">x</span></span></span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">uint</span></span> <span class="t Pointer">*</span><span class="i">yl</span> = <span class="e Cast"><span class="k">cast</span>(<span class="t Integral"><span class="k">uint</span></span> <span class="t Pointer">*</span>)<span class="e Address">&amp;<span class="e Identifier"><span class="i">y</span></span></span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">uint</span></span> <span class="i">m</span> = <span class="e URShift"><span class="e Paren">(<span class="e Plus"><span class="e Paren">(<span class="e And"><span class="e Paren">(<span class="e Deref">*<span class="e Identifier"><span class="i">xl</span></span></span>)</span> &amp; <span class="e Int"><span class="n">0x7FFF_FFFF</span></span></span>)</span> + <span class="e Paren">(<span class="e And"><span class="e Paren">(<span class="e Deref">*<span class="e Identifier"><span class="i">yl</span></span></span>)</span> &amp; <span class="e Int"><span class="n">0x7FFF_FFFF</span></span></span>)</span></span>)</span> &gt;&gt;&gt; <span class="e Int"><span class="n">1</span></span></span>;</span></span>
        <span class="s Expression"><span class="e OrAssign"><span class="e Identifier"><span class="i">m</span></span> |= <span class="e Paren">(<span class="e And"><span class="e Paren">(<span class="e Deref">*<span class="e Identifier"><span class="i">xl</span></span></span>)</span> &amp; <span class="e Int"><span class="n">0x8000_0000</span></span></span>)</span></span>;</span>
        <span class="s Expression"><span class="e Assign"><span class="e Deref">*<span class="e Identifier"><span class="i">ul</span></span></span> = <span class="e Identifier"><span class="i">m</span></span></span>;</span>
    }</span> <span class="k">else</span> <span class="s Compound">{
        <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Int"><span class="n">0</span></span>, <span class="e String"><span class="sl">"Not implemented"</span></span>)</span>;</span>
    }</span></span></span></span></span>
    <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">u</span></span>;</span>
}</span></span></span></span></span>

<span class="d Unittest"><span class="k">unittest</span> <span class="s FuncBody"><span class="s Compound">{
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Rel"><span class="e Call"><span class="e Identifier"><span class="i">ieeeMean</span></span>(-<span class="n">0.0</span>,-<span class="n">1e-20</span>)</span>&lt;<span class="e Int"><span class="n">0</span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Rel"><span class="e Call"><span class="e Identifier"><span class="i">ieeeMean</span></span>(<span class="n">0.0</span>,<span class="n">1e-20</span>)</span>&gt;<span class="e Int"><span class="n">0</span></span></span>)</span>;</span>

    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">ieeeMean</span></span>(<span class="n">1.0L</span>,<span class="n">4.0L</span>)</span>==<span class="e Int"><span class="n">2L</span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">ieeeMean</span></span>(<span class="n">2.0</span>*<span class="n">1.013</span>,<span class="n">8.0</span>*<span class="n">1.013</span>)</span>==<span class="e Mul"><span class="e Int"><span class="n">4</span></span>*<span class="e Real"><span class="n">1.013</span></span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">ieeeMean</span></span>(-<span class="n">1.0L</span>,-<span class="n">4.0L</span>)</span>==<span class="e Sign">-<span class="e Int"><span class="n">2L</span></span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">ieeeMean</span></span>(-<span class="n">1.0</span>,-<span class="n">4.0</span>)</span>==<span class="e Sign">-<span class="e Int"><span class="n">2</span></span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">ieeeMean</span></span>(-<span class="n">1.0f</span>,-<span class="n">4.0f</span>)</span>==<span class="e Sign">-<span class="e Real"><span class="n">2f</span></span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">ieeeMean</span></span>(-<span class="n">1.0</span>,-<span class="n">2.0</span>)</span>==<span class="e Sign">-<span class="e Real"><span class="n">1.5</span></span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">ieeeMean</span></span>(-<span class="n">1</span>*(<span class="n">1</span>+<span class="n">8</span>*<span class="k">real</span>.<span class="i">epsilon</span>),-<span class="n">2</span>*(<span class="n">1</span>+<span class="n">8</span>*<span class="k">real</span>.<span class="i">epsilon</span>))</span>
                 ==<span class="e Mul"><span class="e Sign">-<span class="e Real"><span class="n">1.5</span></span></span>*<span class="e Paren">(<span class="e Plus"><span class="e Int"><span class="n">1</span></span>+<span class="e Mul"><span class="e Int"><span class="n">5</span></span>*<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">epsilon</span></span></span></span>)</span></span></span>)</span>;</span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">ieeeMean</span></span>(<span class="n">0x1p60</span>,<span class="n">0x1p-10</span>)</span>==<span class="e Real"><span class="n">0x1p25</span></span></span>)</span>;</span>
    <span class="s StaticIf"><span class="k">static</span> <span class="k">if</span> (<span class="e Equal"><span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">mant_dig</span></span>==<span class="e Int"><span class="n">64</span></span></span>) <span class="s Compound">{ <span class="lc">// x87, 80-bit reals</span>
      <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">ieeeMean</span></span>(<span class="n">1.0L</span>,<span class="k">real</span>.<span class="i">infinity</span>)</span>==<span class="e Real"><span class="n">0x1p8192L</span></span></span>)</span>;</span>
      <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">ieeeMean</span></span>(<span class="n">0.0L</span>,<span class="k">real</span>.<span class="i">infinity</span>)</span>==<span class="e Real"><span class="n">1.5</span></span></span>)</span>;</span>
    }</span></span>
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">ieeeMean</span></span>(<span class="n">0.5</span>*<span class="k">real</span>.<span class="i">min</span>*(<span class="n">1</span>-<span class="n">4</span>*<span class="k">real</span>.<span class="i">epsilon</span>),<span class="n">0.5</span>*<span class="k">real</span>.<span class="i">min</span>)</span>
           == <span class="e Mul"><span class="e Mul"><span class="e Real"><span class="n">0.5</span></span>*<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">min</span></span></span>*<span class="e Paren">(<span class="e Minus"><span class="e Int"><span class="n">1</span></span>-<span class="e Mul"><span class="e Int"><span class="n">2</span></span>*<span class="e TypeDotId"><span class="t Integral"><span class="k">real</span></span>.<span class="i">epsilon</span></span></span></span>)</span></span></span>)</span>;</span>
}</span></span></span>

<span class="d Protection"><span class="k">public</span>:


<span class="bc">/***********************************
 * Evaluate polynomial A(x) = $(SUB a, 0) + $(SUB a, 1)x + $(SUB a, 2)&amp;sup2;
 *                          + $(SUB a,3)x&amp;sup3; ...
 *
 * Uses Horner's rule A(x) = $(SUB a, 0) + x($(SUB a, 1) + x($(SUB a, 2)
 *                         + x($(SUB a, 3) + ...)))
 * Params:
 *      A =     array of coefficients $(SUB a, 0), $(SUB a, 1), etc.
 */</span>
<span class="d Compound"><span class="d Function"><span class="t Integral"><span class="k">real</span></span> <span class="i">poly</span><span class="o Parameters">(<span class="o Parameter"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span></span>, <span class="o Parameter"><span class="t Integral"><span class="k">real</span></span><span class="t Array">[]</span> <span class="i">A</span></span>)</span>
<span class="s FuncBody"><span class="k">in</span>
<span class="s Compound">{
    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>(<span class="e Rel"><span class="e Dot"><span class="e Identifier"><span class="i">A</span></span>.<span class="e Identifier"><span class="i">length</span></span></span> &gt; <span class="e Int"><span class="n">0</span></span></span>)</span>;</span>
}</span>
<span class="k">body</span>
<span class="s Compound">{
    <span class="s Version"><span class="k">version</span> (<span class="i">D_InlineAsm_X86</span>)
    <span class="s Compound">{
        <span class="s Version"><span class="k">version</span> (<span class="i">Windows</span>)
        <span class="s Compound">{
        <span class="lc">// BUG: This code assumes a frame pointer in EBP.</span>
            <span class="s AsmBlock"><span class="k">asm</span> <span class="lc">// assembler by W. Bright</span>
            {
                <span class="lc">// EDX = (A.length - 1) * real.sizeof</span>
                <span class="s Asm"><span class="i">mov</span>     <span class="e AsmRegister"><span class="i">ECX</span></span>,<span class="e AsmPostBracket"><span class="e Identifier"><span class="i">A</span></span>[<span class="e AsmRegister"><span class="i">EBP</span></span>]</span>              ;</span> <span class="lc">// ECX = A.length</span>
                <span class="s Asm"><span class="i">dec</span>     <span class="e AsmRegister"><span class="i">ECX</span></span>                     ;</span>
                <span class="s Asm"><span class="i">lea</span>     <span class="e AsmRegister"><span class="i">EDX</span></span>,<span class="e AsmPostBracket"><span class="e AsmBracket">[<span class="e AsmRegister"><span class="i">ECX</span></span>]</span>[<span class="e Mul"><span class="e AsmRegister"><span class="i">ECX</span></span>*<span class="e Int"><span class="n">8</span></span></span>]</span>        ;</span>
                <span class="s Asm"><span class="i">add</span>     <span class="e AsmRegister"><span class="i">EDX</span></span>,<span class="e AsmRegister"><span class="i">ECX</span></span>                 ;</span>
                <span class="s Asm"><span class="i">add</span>     <span class="e AsmRegister"><span class="i">EDX</span></span>,<span class="e Plus"><span class="e Identifier"><span class="i">A</span></span>+<span class="e AsmPostBracket"><span class="e Int"><span class="n">4</span></span>[<span class="e AsmRegister"><span class="i">EBP</span></span>]</span></span>            ;</span>
                <span class="s Asm"><span class="i">fld</span>     <span class="e AsmType"><span class="k">real</span> <span class="i">ptr</span> <span class="e AsmBracket">[<span class="e AsmRegister"><span class="i">EDX</span></span>]</span></span>          ;</span> <span class="lc">// ST0 = coeff[ECX]</span>
                <span class="s Asm"><span class="i">jecxz</span>   <span class="e Identifier"><span class="i">return_ST</span></span>               ;</span>
                <span class="s Asm"><span class="i">fld</span>     <span class="e AsmPostBracket"><span class="e Identifier"><span class="i">x</span></span>[<span class="e AsmRegister"><span class="i">EBP</span></span>]</span>                  ;</span> <span class="lc">// ST0 = x</span>
                <span class="s Asm"><span class="i">fxch</span>    <span class="e AsmRegister"><span class="i">ST</span>(<span class="n">1</span>)</span>                   ;</span> <span class="lc">// ST1 = x, ST0 = r</span>
                <span class="s AsmAlign"><span class="k">align</span>   <span class="n">4</span>                       ;</span>
        <span class="s Labeled"><span class="i">L2</span>:     <span class="s Asm"><span class="i">fmul</span>    <span class="e AsmRegister"><span class="i">ST</span></span>,<span class="e AsmRegister"><span class="i">ST</span>(<span class="n">1</span>)</span>                ;</span></span> <span class="lc">// r *= x</span>
                <span class="s Asm"><span class="i">fld</span>     <span class="e AsmType"><span class="k">real</span> <span class="i">ptr</span> <span class="e AsmPostBracket"><span class="e Sign">-<span class="e Int"><span class="n">10</span></span></span>[<span class="e AsmRegister"><span class="i">EDX</span></span>]</span></span>       ;</span>
                <span class="s Asm"><span class="i">sub</span>     <span class="e AsmRegister"><span class="i">EDX</span></span>,<span class="e Int"><span class="n">10</span></span>                  ;</span> <span class="lc">// deg--</span>
                <span class="s Asm"><span class="i">faddp</span>   <span class="e AsmRegister"><span class="i">ST</span>(<span class="n">1</span>)</span>,<span class="e AsmRegister"><span class="i">ST</span></span>                ;</span>
                <span class="s Asm"><span class="i">dec</span>     <span class="e AsmRegister"><span class="i">ECX</span></span>                     ;</span>
                <span class="s Asm"><span class="i">jne</span>     <span class="e Identifier"><span class="i">L2</span></span>                      ;</span>
                <span class="s Asm"><span class="i">fxch</span>    <span class="e AsmRegister"><span class="i">ST</span>(<span class="n">1</span>)</span>                   ;</span> <span class="lc">// ST1 = r, ST0 = x</span>
                <span class="s Asm"><span class="i">fstp</span>    <span class="e AsmRegister"><span class="i">ST</span>(<span class="n">0</span>)</span>                   ;</span> <span class="lc">// dump x</span>
                <span class="s AsmAlign"><span class="k">align</span>   <span class="n">4</span>                       ;</span>
        <span class="s Labeled"><span class="i">return_ST</span>:                              <span class="s Empty">;</span></span>
                <span class="s Empty">;</span>
            }</span>
        }</span>
        <span class="k">else</span>
        <span class="s Compound">{
            <span class="s AsmBlock"><span class="k">asm</span> <span class="lc">// assembler by W. Bright</span>
            {
                <span class="lc">// EDX = (A.length - 1) * real.sizeof</span>
                <span class="s Asm"><span class="i">mov</span>     <span class="e AsmRegister"><span class="i">ECX</span></span>,<span class="e AsmPostBracket"><span class="e Identifier"><span class="i">A</span></span>[<span class="e AsmRegister"><span class="i">EBP</span></span>]</span>              ;</span> <span class="lc">// ECX = A.length</span>
                <span class="s Asm"><span class="i">dec</span>     <span class="e AsmRegister"><span class="i">ECX</span></span>                     ;</span>
                <span class="s Asm"><span class="i">lea</span>     <span class="e AsmRegister"><span class="i">EDX</span></span>,<span class="e AsmBracket">[<span class="e Mul"><span class="e AsmRegister"><span class="i">ECX</span></span>*<span class="e Int"><span class="n">8</span></span></span>]</span>             ;</span>
                <span class="s Asm"><span class="i">lea</span>     <span class="e AsmRegister"><span class="i">EDX</span></span>,<span class="e AsmPostBracket"><span class="e AsmBracket">[<span class="e AsmRegister"><span class="i">EDX</span></span>]</span>[<span class="e Mul"><span class="e AsmRegister"><span class="i">ECX</span></span>*<span class="e Int"><span class="n">4</span></span></span>]</span>        ;</span>
                <span class="s Asm"><span class="i">add</span>     <span class="e AsmRegister"><span class="i">EDX</span></span>,<span class="e Plus"><span class="e Identifier"><span class="i">A</span></span>+<span class="e AsmPostBracket"><span class="e Int"><span class="n">4</span></span>[<span class="e AsmRegister"><span class="i">EBP</span></span>]</span></span>            ;</span>
                <span class="s Asm"><span class="i">fld</span>     <span class="e AsmType"><span class="k">real</span> <span class="i">ptr</span> <span class="e AsmBracket">[<span class="e AsmRegister"><span class="i">EDX</span></span>]</span></span>          ;</span> <span class="lc">// ST0 = coeff[ECX]</span>
                <span class="s Asm"><span class="i">jecxz</span>   <span class="e Identifier"><span class="i">return_ST</span></span>               ;</span>
                <span class="s Asm"><span class="i">fld</span>     <span class="e AsmPostBracket"><span class="e Identifier"><span class="i">x</span></span>[<span class="e AsmRegister"><span class="i">EBP</span></span>]</span>                  ;</span> <span class="lc">// ST0 = x</span>
                <span class="s Asm"><span class="i">fxch</span>    <span class="e AsmRegister"><span class="i">ST</span>(<span class="n">1</span>)</span>                   ;</span> <span class="lc">// ST1 = x, ST0 = r</span>
                <span class="s AsmAlign"><span class="k">align</span>   <span class="n">4</span>                       ;</span>
        <span class="s Labeled"><span class="i">L2</span>:     <span class="s Asm"><span class="i">fmul</span>    <span class="e AsmRegister"><span class="i">ST</span></span>,<span class="e AsmRegister"><span class="i">ST</span>(<span class="n">1</span>)</span>                ;</span></span> <span class="lc">// r *= x</span>
                <span class="s Asm"><span class="i">fld</span>     <span class="e AsmType"><span class="k">real</span> <span class="i">ptr</span> <span class="e AsmPostBracket"><span class="e Sign">-<span class="e Int"><span class="n">12</span></span></span>[<span class="e AsmRegister"><span class="i">EDX</span></span>]</span></span>       ;</span>
                <span class="s Asm"><span class="i">sub</span>     <span class="e AsmRegister"><span class="i">EDX</span></span>,<span class="e Int"><span class="n">12</span></span>                  ;</span> <span class="lc">// deg--</span>
                <span class="s Asm"><span class="i">faddp</span>   <span class="e AsmRegister"><span class="i">ST</span>(<span class="n">1</span>)</span>,<span class="e AsmRegister"><span class="i">ST</span></span>                ;</span>
                <span class="s Asm"><span class="i">dec</span>     <span class="e AsmRegister"><span class="i">ECX</span></span>                     ;</span>
                <span class="s Asm"><span class="i">jne</span>     <span class="e Identifier"><span class="i">L2</span></span>                      ;</span>
                <span class="s Asm"><span class="i">fxch</span>    <span class="e AsmRegister"><span class="i">ST</span>(<span class="n">1</span>)</span>                   ;</span> <span class="lc">// ST1 = r, ST0 = x</span>
                <span class="s Asm"><span class="i">fstp</span>    <span class="e AsmRegister"><span class="i">ST</span>(<span class="n">0</span>)</span>                   ;</span> <span class="lc">// dump x</span>
                <span class="s AsmAlign"><span class="k">align</span>   <span class="n">4</span>                       ;</span>
        <span class="s Labeled"><span class="i">return_ST</span>:                              <span class="s Empty">;</span></span>
                <span class="s Empty">;</span>
            }</span>
        }</span></span>
    }</span>
    <span class="k">else</span>
    <span class="s Compound">{
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">int</span></span> <span class="i">i</span> = <span class="e Minus"><span class="e Dot"><span class="e Identifier"><span class="i">A</span></span>.<span class="e Identifier"><span class="i">length</span></span></span> - <span class="e Int"><span class="n">1</span></span></span>;</span></span>
        <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">r</span> = <span class="e Index"><span class="e Identifier"><span class="i">A</span></span>[<span class="e Identifier"><span class="i">i</span></span>]</span>;</span></span>
        <span class="s While"><span class="k">while</span> (<span class="e Rel"><span class="e PreDecr">--<span class="e Identifier"><span class="i">i</span></span></span> &gt;= <span class="e Int"><span class="n">0</span></span></span>)
        <span class="s Compound">{
            <span class="s Expression"><span class="e MulAssign"><span class="e Identifier"><span class="i">r</span></span> *= <span class="e Identifier"><span class="i">x</span></span></span>;</span>
            <span class="s Expression"><span class="e PlusAssign"><span class="e Identifier"><span class="i">r</span></span> += <span class="e Index"><span class="e Identifier"><span class="i">A</span></span>[<span class="e Identifier"><span class="i">i</span></span>]</span></span>;</span>
        }</span></span>
        <span class="s Return"><span class="k">return</span> <span class="e Identifier"><span class="i">r</span></span>;</span>
    }</span></span>
}</span></span></span>

<span class="d Unittest"><span class="k">unittest</span>
<span class="s FuncBody"><span class="s Compound">{
    <span class="s Debug"><span class="k">debug</span> (<span class="i">math</span>) <span class="s Expression"><span class="e Call"><span class="e Identifier"><span class="i">printf</span></span>(<span class="sl">"math.poly.unittest\n"</span>)</span>;</span></span>
    <span class="s Declaration"><span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">x</span> = <span class="e Real"><span class="n">3.1</span></span>;</span></span>
    <span class="d StorageClass"><span class="k">static</span> <span class="d Variables"><span class="t Integral"><span class="k">real</span></span> <span class="i">pp</span><span class="t Array">[]</span> = <span class="e ArrayInit">[<span class="e Real"><span class="n">56.1</span></span>, <span class="e Real"><span class="n">32.7</span></span>, <span class="e Int"><span class="n">6</span></span>]</span>;</span></span>

    <span class="s Expression"><span class="e Assert"><span class="k">assert</span>( <span class="e Equal"><span class="e Call"><span class="e Identifier"><span class="i">poly</span></span>(<span class="i">x</span>, <span class="i">pp</span>)</span> == <span class="e Paren">(<span class="e Plus"><span class="e Real"><span class="n">56.1L</span></span> + <span class="e Mul"><span class="e Paren">(<span class="e Plus"><span class="e Real"><span class="n">32.7L</span></span> + <span class="e Mul"><span class="e Int"><span class="n">6L</span></span> * <span class="e Identifier"><span class="i">x</span></span></span></span>)</span> * <span class="e Identifier"><span class="i">x</span></span></span></span>)</span></span> )</span>;</span>
}</span></span></span></span></span></span></span></span></span></span></span></span>

</pre></td>
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